How to Simplify a Square Root in 3 Easy Steps

How to Simplify a Square Root in 3 Easy Steps

How to Simplify a Square Root

Step-by-Step Guide: How to Simplify a Square Root in 3 Steps

 

Free Step-by-Step Guide: Ready to learn how to simplify a square root?

 

Simplifying square roots is a useful and important math skill that every student can learn with enough practice. By learning a simple 3-step process for simplifying square roots, you can learn to quickly and correctly simplify any square root (whether it is a perfect square or not), and that is exactly what we will be doing in this free guide.

The sections below will teach you exactly how to simplify a square root using a simple step-by-step method. Together, we will recap some key concepts and vocabulary terms and then work through three examples of how to simplify a square root. Whether you are learning this skill for the very first time or you are an experienced student in need of a quick and comprehensive review, this page will share everything you need to know about how to simplify a square root.

This guide is organized based on the following sections:

You can use the text links above to jump to any section of this guide, or you can work through the sections in order. Let’s get started!

 

Preview: How to Simplify a Square Root in 3 Steps.

 

Quick Intro: Square Roots and Perfect Squares

Before we work through examples of how to simplify a square root, let’s quickly recap some important concepts and vocabulary terms related to this topic.

In math, square roots are the inverse (or opposite) operation of squaring a number (i.e. multiplying a number by itself). And, conversely, the square root of a number is the value that, when multiplied by itself, results in the number that you started with.

For example, consider the square root of 16, which can be expressed using square root notation:

  • √16

We can say that √16 equals 4 because 4 times itself (i.e. 4x4 or 4²) equals 16, therefore:

  • √16 = 4 → because 4² = 16

Numbers like 16 are called perfect squares because their square roots are whole numbers, which makes them very easy to simplify.

In fact, you are likely already familiar with how to simplify many perfect squares such as:

  • √4 = 2 → because 2² = 4

  • √9 = 3 → because 3² = 9

  • √16 = 4 → because 4² = 16

  • √25 = 5 → because 5² = 25

  • √36 = 6 → because 6² = 36

  • √49 = 7 → because 7² = 49

  • √64 = 8 → because 8² = 64

  • √81 = 9 → because 9² = 81

  • √100 = 10 → because 10² = 100

Figure 01: Perfect Squares up to 144

Make sure that you know all of the perfect squares from 1 to 144 (as shown in Figure 01 above) before moving onto the next section.

While it is relatively easy to simplify a square root of a perfect square, it is more complicated to simplify a square root of a non-perfect square, which is what we will be focusing on in the next section, where, for example, we will look at finding the perfect squares of numbers like 18, 75, and 112.

How to Simplify a Square Root Examples

Now we are ready to use the following simple 3-step method for simplifying square roots to solve three practice problems:

Steps: How to Simplify a Square Root

  • Step 1: Identify two factors where one of them is a perfect square (choose the largest perfect square factor), and rewrite as a product.

  • Step 2: Split the product using two square root symbols.

  • Step 3: Simplify the perfect square and rewrite your final answer.

Example A: Simplify √18

 

Example A: Simplify √18

In our first example, we want to simplify a square root of a non-perfect square: √18.

We can simplify a square root like √18 by using our three step strategy as follows:

Step 1: Identify two factors where one of them is a perfect square.

Let’s start by listing the factors of 18:

  • Factors of 18: 1, 2, 3, 6, 9 and 18

Notice that 18 has one factor that is a perfect square: 9, and that:

  • 9 x 2 = 18

Since 9 x 2 equals 18, the two numbers that we are going to use for Step 2 are 9 and 2.

Step 2: Split the product using two square root symbols.

For the second step, we can use the factors from Step 1 to rewrite √18 as follows:

  • √18 = √(9 x 2) = √9 x √2

We can “split” the square root in this way because of the product property of square roots, which says that:

  • √(A x B) = √(A) x √(B)

(provided that A and B are non-negative numbers).

So we now have a new equivalent product that represents √18, which is…

  • √9 x √2

Step 3: Simplify the perfect square and rewrite your final answer.

For our final step, notice that one of the square roots in our new expression, √9, is a perfect square. Since we know that √9 = 3, we can rewrite √9 as 3 as follows:

  • √9 x √2 = 3 x √2

Now, all that we have to do is rewrite the result, 3 x √2, as 3√2 , and we have solved the problem!

Final Answer: √18 = 3√2

Figure 02 below shows the step-by-step process for simplifying this square root.

 

Figure 02: How to Simplify a Square Root in 3 Steps.

 

Now that you have learned how to simplify a square root, let’s gain some more experience by working through another example.

Example B: Simplify √75

 

Example B: Simplify √75

We can solve this next example by using the three steps that we used to solve the previous example.

Step 1: Identify the factors of 75 and determine the largest perfect square factor.

We can begin by listing the factors of 75:

  • Factors of 75: 1, 3, 5, 15, 25 and 75

Notice that 75 has one perfect square factor, 25, and that:

  • 25 x 3 = 75

Step 2: Split the product using two square root symbols.

Next, we can use the factors from Step 1 to rewrite √75as follows:

  • √75 = √(25 x 3) = √25 x √3

Step 3: Simplify and solve.

Finally, we can simplify √25 as 5 (since √25=5) and rewrite the expression as follows:

  • √25 x √3 = 5 x √3

We can now rewrite 5 x √3 as 5√3 and we can conclude that:

Final Answer: √75 = 5√3

The entire process for solving this problem is shown in Figure 03 below.

 

Figure 03: Multiplying fractions with whole numbers Example B solved.

 

Example C: Simplify √112

 

Example C: Simplify √112

For our final step-by-step example of how to simplify a square root, let’s take on a triple-digit number using our three-step method.

Step 1: Identify the factors of 112 and pick out the largest perfect square factor.

  • Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56 and 112

Notice 112 has two perfect square factors: 4 and 16. In cases like this, always choose the largest perfect square factor (16 in this case).

Now that we have identified our perfect square factor, we can say that:

  • w16 x 7 = 112

Step 2: Split the product using two square root symbols.

Next, we can write √112 as follows:

  • √112 = √(16 x 7) = √16 x √7

Step 3: Simplify and solve.

For the final step, we can simplify √16 as 4 and rewrite the expression as follows:

  • √16 x √7 = 4 x √7

Now we just have to rewrite 4 x √7 as 4√7 and we have solved the problem!

Final Answer: √112 = 4√7

The three-step process for solving Example C is shown in Figure 03 below

 

Figure 03: How to Simplify a Square Root in 3 Steps.

 
 
 

More Free Math Resources:

How to Multiply Fractions with Whole Numbers—Step-by-Step

How to Multiply Fractions with Whole Numbers—Step-by-Step

How to Multiply Fractions with Whole Numbers

Step-by-Step Guide: How to Multiply Fractions with Whole Numbers, Multiplying Fractions by Whole Numbers Examples

 

Free Step-by-Step Guide: How to multiply fractions with whole numbers explained.

 

Multiplying fractions with whole numbers can seem like a challenging math skill, but, with some simple strategies and an easy step-by-step method, it can be a relatively easy task that any student can master.

In this free guide, we will work through several examples of how to multiply fractions with whole numbers using a simple step-by-step process. As long as you can follow three easy steps, you will be able to confidently and accurately solve a variety of math problems where you have to multiply fractions with whole numbers.

You can work through the sections in this free guide in sequential order, or you can click on any of the quick-links below to jump to one particular section.

Quick Intro: Multiply Fractions with Whole Numbers

Before we dive into any examples of how to multiply fractions with whole numbers, let’s do a quick introductory review of what it means when we multiply fractions with whole numbers.

For example, let’s consider the example 3 x 1/4:

  • 3 is the whole number

  • 1/4 is the fraction

Whenever you multiply a fraction by a whole number, you are really just performing repeated addition (i.e. you are adding the fraction to itself a number of repeated times that is determined by the whole number).

If we think of multiplication in terms of repeated addition, we can rewrite 3 x 1/4 as follows:

  • 3 x 1/4 = 1/4 + 1/4 + 1/4

And, since 1/4 + 1/4 + 1/4 is equal to 3/4, we can conclude that:

  • 3 x 1/4 = 1/4 + 1/4 + 1/4 = 3/4

Final Answer: 3 x 1/4 = 3/4

 

Figure 01: How to Multiply Fractions with Whole Numbers Using Repeated Addition.

 

The process of multiplying fractions with whole numbers using repeated addition is shown in Figure 01.

While we will not use repeated addition to solve the examples in this guide, understanding this basic relationship between multiplication and repeated addition is the first step to easily learning how to multiply fractions with whole numbers.

Now, let’s go ahead and work through some examples of multiplying fractions with whole numbers using a simple 3-step method.

Multiplying Fractions by Whole Numbers Examples

For all of the multiplying fractions with whole numbers examples that follow, we will be using the following 3-step method for solving:

  • Step 1: Rewrite the whole number as a fraction with a denominator of 1.

  • Step 2: Multiply the numerators together and then multiply the denominators together.

  • Step 3: Simplify if possible.

 

Example A: Multiplying whole numbers with fractions.

 

Example A: Multiply 2 x 1/3

For our first example, we have to multiply the whole number 2 by the fraction ⅓, and we will do that by following our 3-step process as follows:

Step 1: Rewrite the whole number as a fraction with a denominator of 1.

First, we can rewrite the whole number, 2, as a fraction with a numerator of 1 as follows:

  • 2 → 2/1

Now we have a new multiplication problem:

  • 2 x 1/3 → 2/1 x 1/3

Step 2: Multiply the numerators together and then multiply the denominators together.

Now that we have a new expression with two fractions being multiplied by each other, we can perform multiplication by multiplying the numerators together and then multiplying the denominators together as follows:

  • 2/1 x 1/3 = (2x1) / (1x3) = 2/3

After completing Step 2, we are left with the fraction 2/3.

Step 3: Simplify if possible.

Finally, we just have to check if our result from Step 2, 2/3, can be simplified.

In this case, the fraction 2/3 can not be simplified because there is no common factor between the numerator (2) and the denominator (3) other than 1.

Final Answer: 2 x 1/3 = 2/3
The complete step-by-step process for solving this first example is shown in Figure 02 below.

 

Figure 02: How to multiply fractions with whole numbers step-by-step.

 

Now that you are familiar with our 3-step method for multiplying fractions with whole numbers, let’s gain some more experience by using them to solve another example.

 

Example B: 2/3 × 34 = ?

 

Example B: Multiply 2/3 x 4

For this next example, notice how, in this case, the first term is a fraction and the second term is the whole number (this is a reverse situation compared to Example A). However, the commutative property of multiplication tells us that the order of the terms does not matter, so we can still use our 3-step process to solve this problem as follows:

Step 1: Rewrite the whole number as a fraction with a denominator of 1.

We can leave the fraction 2/3 alone and rewrite the whole number 4 as a fraction with a denominator of 1 as follows:

  • 2/3 x 4 → 2/3 x 4/1

Step 2: Multiply the numerators together and then multiply the denominators together.

Next, we can take our new expression and simply multiply the numerators together, and then the denominators together as follows:

  • 2/3 x 4/1 = (2x4) / (3x1)

  • (2x4) / (3x1) = 8/3

After completing the second step, our result is 8/3. We can now move onto the third and final step.

Step 3: Simplify if possible.

Let’s see if our result from Step 2, 8/3, can be simplified.

Since there is no common factor (other than 1) between the numerator (8) and the denominator (3), we know that the fraction 8/3 can not be simplified. However, since 8/3 is an improper fraction, we do have the option of either expressing it as 8/3 or as the mixed number 2 2/3 (in this case, we will choose to express our answer as 8/3).

Final Answer: 2/3 x 4 = 8/3
Figure 03 below illustrates our step-by-step process for solving this second example.

 

Figure 03: Multiplying fractions with whole numbers Example B solved.

 
 

5Example C: 10 × 1/5 = ?

 

Example C: Multiply 10 x 1/5

Let’s gain some more practice using our 3-step method for multiplying fractions with whole numbers.

Step 1: Rewrite the whole number as a fraction with a denominator of 1.

In this example, we have to rewrite the whole number (10) as a fraction with a denominator of 1.

  • 10 x 1/5 → 10/1 x 1/5

Step 2: Multiply the numerators together and then multiply the denominators together.

Next, let’s take our new expression, 10/1 x 1/5, and multiply the numerators and denominators together:

  • 10/1 x 1/5 = (10x1) / (1x5)

  • (10x1) / (1x5) = 10/5

Finally, let’s move onto Step 3 to see if our result (10/5) can be simplified.

Step 3: Simplify if possible.

In this case, the numerator (10) and the denominator (5) share a common factor of 5. So, we can simplify 10/5 by dividing both the numerator and denominator by 5 as follows:

  • 10 ÷ 5 = 2

  • 5 ÷ 5 = 1

After dividing, we can say that 10/5 = 2/1, and we can rewrite 2/1 as 2.

Final Answer: 10 x 1/5 = 10/5 = 2/1 = 2
The entire process of solving Example C is shown in Figure 04 below illustrates our step-by-step process for solving this second example.

 

Figure 05: Example C Solved.

 
 

Example D: 7 × 5/6 = ?

 

Example D: Multiply 7 x 5/6

Let’s work through one final example of multiplying fractions with whole numbers.

Step 1: Rewrite the whole number as a fraction with a denominator of 1.

In this case, we can rewrite the whole number (7) as a fraction as follows:

  • 7 x 5/6 → 7/1 x 5/6

Step 2: Multiply the numerators together and then multiply the denominators together.

Next, we can multiply the two fractions together as follows:

  • 7/1 x 5/6 = (7x5) / (1x6)

  • (7x5) / (1x6) = 35/6

Step 3: Simplify if possible.

Finally, we have to see if our result from Step 2 (35/6) can be simplified. Since 35 and 6 do not share any common factors besides 1, we know that it can not be simplified any further.

Final Answer: 7 x 5/6 = 35/6
Figure 06 shows how we solved this final example.

 

Figure 06: How to Multiply Fractions with Whole Numbers.

 
 
 

More Free Math Resources:

How to Factor Polynomials—Step-by-Step Examples and Tutorial

How to Factor Polynomials—Step-by-Step Examples and Tutorial

How to Factor Polynomials Explained

Factoring polynomials is a process of rewriting a polynomial as the product of one or more simpler expressions—including constants, variables, or factors that can not be further reduced. How to factor a given polynomial will depend on a few different factors, including the number of terms, the value of the coefficients, and the structure of the polynomial.

 

Free Step-by-Step Guide: How to factor a polynomial with a specific number of terms

 
Anthony Persico

by Anthony Persico

Founder & Head Educator, Mashup Math
With a background in elementary and secondary math education and special education, Anthony has taught thousands of K-12 students across the United States.

Learn more about the author →

Last Updated: May 2025

In algebra, a polynomial is an expression made up of variables and coefficients separated by the operations of addition and/or subtraction.

Polynomials are a fundamental math topic and understanding how to work with them (including factoring) is essential to being successful in algebra and beyond. Learning how to factor polynomials with 2, 3, or 4 terms involves understanding how to break down a given polynomial into simpler factors.

This free Step-by-Step Guide on How to Factor Polynomials will cover the following topics:

Table of Contents

While learning how to factor polynomials can be challenging, it is a learnable skill that can be acquired through practice. The goal of this free guide on how to factor polynomials is to give you plenty of step-by-step practice with factoring polynomials—including polynomials with 4 terms (cubic polynomials)—so that can become more comfortable with factoring all kinds of polynomials.

Before we cover everything you need to know about how to factor a polynomial, let’s quickly recap some key algebra vocabulary terms and phrases that you will need to be familiar with in order to use this guide.

 

Figure 01: How to Factor Polynomials: What is a Polynomial?

 

What is a polynomial?

As previously stated, a polynomial is a math expression comprised of variables, coefficients, and/or constants separated by the operations of addition or subtraction.

The terms of polynomials are individual parts, or monomials, separated by addition or subtraction signs.

For example,

  • 3x² is a monomial

  • 3x² + 6x is a polynomial with 2 terms (3x² and 6x)

  • 3x² + 6x - 15 is a polynomial with 3 terms (3x², 6x, and -15)

  • 9x³ + 3x² + 6x - 15 is a polynomial with 4 terms (9x³, 3x², 6x, and -15)

Figure 01 above illustrates the difference between a monomial and a polynomial.

For an expression to be considered a polynomial, it must have at least two terms, but there is no limit on how many terms a polynomial can have.

When it comes to factoring polynomials, you will most commonly be dealing with polynomials that have 2 terms, 3 terms, or 4 terms:

  • A polynomial with 2 terms is called a binomial

  • A polynomial with 3 terms is called a trinomial

  • A polynomial with 4 terms is called a quadrinomial (also known as a cubic polynomial)

Examples of a polynomial with 2 terms, 3 terms, and 4 terms are shown in Figure 02 below.

 

Figure 02: How to factor polynomials with 4 terms or less.

 

Now that you understand the key terms and the difference between a polynomial with 2 terms, 3 terms, and 4 terms.

For factoring each type of polynomial, we will look at two methods: GCF, direct factoring, and a combination of the two.

Let’s get started!

How to Factor Polynomials with 2 Terms

We will start by learning how to factor polynomials with 2 terms (binomials).

Whenever you are factoring a polynomial with any number of terms, it is always best to start by looking to see if there is a GCF—or greatest common factor—that all of the terms have in common.

For example, consider the following example:

Example #1: Factor 8x + 4

For this example, you should notice that both terms, 8x and 4 are divisible by 4, hence they share a GCF of 4.

Therefore, you can divide out the GCF of 4 from both terms as follows:

  • 8x + 4 → 4 (2x + 1)

So, the factors of 8x + 4 are: 4 and (2x+1).

What we just did was essentially the reverse of the distributive property, as shown in Figure 03 below.

 

Figure 03: How to factor a polynomial with 2 terms using the GCF method.

 

Note that many binomials can be factored using the GCF method, so let’s gain a little more practice with one more example (understanding how to simplify and/or factor a polynomial using the GCF method will come in handy when you start factoring 3 and 4 term polynomials later on).

Example #2: Factor 6x² + 12x

Just like the first example, there is a GCF for both terms. But, in this case, the GCF includes a variable. Why? Because both terms have coefficients that are divisible by 6 and both terms have at least one x variable, so the GCF, in this case, is 6x.

Therefore, you can divide out 6x from both terms as follows:

  • 6x² + 12x → 6x(x + 2)

So, the factors of 6x² + 12x are: 6x and (x+2).

Again, this method of factoring is just the reverse of the distributive property and is illustrated in Figure 04 below.

 

Figure 04: How to factor a polynomial with 2 terms using the GCF method.

 

Next, we will look at a special case of factoring a binomial—when the binomial is a difference of two squares (this is sometimes referred to as DOTS).

Whenever you have a binomial of the form a²-b², the factors will be of the form (a+b)(a-b).

Example #3: Factor x² - 49

For example, if you wanted to factor the binomial: x² - 49, you would notice that both x² and 49 are squares:

  • x² = (x)(x)

  • 49=(7)(7)

So, another way to write (x²- 49) is (x²- 7²)

Therefore, you can use the DOTS method for factoring binomials. In this case, a = x and b = 7, so:

  • (a²-b²) = (a+b)(a-b) → (x²- 7²) = (x-7)(x+7)

You can now conclude that the factors of x²- 49 are (x-7) and (x+7) using the DOTS method.

This process is illustrated in Figure 05 below:

 

Figure 05: How to factor a polynomial that is the difference of two squares.

 

If you want to learn more about the DOTS method for factoring polynomials that are the difference of two squares, check out this free video tutorial on YouTube for more practice.

And if you want more practice, check out our free Factoring Polynomials Worksheet Library, where you can download free PDF practice worksheets with answer keys.

Otherwise, let’s continue onto the next section where you will learn how to factor polynomials with 3 terms.

How to Factor Polynomials with 3 Terms

Moving on, we will now look at polynomials with 3 terms, typically referred to as trinomials

Learning how to factor polynomials with 3 terms involves a more involved factoring process that we will explore in this section.

The trinomials that we will cover will be of the form ax² + bx + c (where c is a constant). The strategies that we will use will depend on whether a (the leading coefficient) equals one or not. Therefore, the first two examples in this section will be factoring trinomials when a=1 and the second two examples will be when a≠1.

How to Factor Polynomials with 3 Terms when a=1

Example #1: Factor x² + 6x + 8

For the first example, we have to factor the trinomial: x² + 6x + 8

 

Figure 06: How to factor polynomials with 3 terms (when a=1)

 

Again, the leading coefficient, a, is equal to 1 in this example. This is important to note because the following method for factoring a trinomial only works when a=1.

Now we are ready to factor this trinomial in 3 easy steps:

Step One: Identify the values of b and c.

In this example, the values of b and c in the trinomial are: b=6 and c=8

Step Two: Figure out two numbers that both ADD to b and MULTIPLY to c.

The second step often involves some of trial-and-error as you pick numbers and see if they meet both conditions (the two numbers have to add together to make b and multiply together to make c).

  • 5 + 1 =6 (the value of b) ✓

  • 5 x 1 ≠ 8 (the value of c) ✘

For example, lets say that you chose the numbers 5 and 1. While 5+1=6 is true (satisfying the first condition), 5x1=5 (not 8), therefore, they do not satisfy the second condition. So, 5 and 1 do not work.

But, if you picked the numbers 2 and 4, you can see that:

  • 2 + 4 =6 (the value of b) ✓

  • 2 x 4 = 8 (the value of c) ✓

Since 2 and 4 satisfy both conditions, you can stop searching and move onto the third step.

Step Three: Use your numbers from step two to write out the factors

In this case, you can conclude that the factors of x² + 6x + 8 are (x+2) and (x+4).

 

Figure 07: The factors of x² + 6x + 8 are (x+2) and (x+4).

 

You can verify that these are the correct factors by performing double distribution as follows:

  • (x+2)(x+4) = x² + 2x + 4x + 8 = x² + 6x + 8

Notice that you ended up with the trinomial that you started with! Now, lets work through one more example of how to factor polynomials with 3 terms when a=1.

Example #2: Factor x² - 3x - 40

For this next example, we have to factor the trinomial: x² - 3x - 40

 

Figure 08: How to factor 3rd degree polynomials

 

Notice that, in this case, the trinomial includes subtraction signs, which will affect how you perform step two below.

Step One: Identify the values of b and c.

For this trinomial, b= -3 and c= -40

Step Two: Figure out two numbers that both ADD to b and MULTIPLY to c.

Again, you have to find two numbers that add to make -3 and that multiply together to make -40.

This part can be tricky when both of the values for b and c are negative (like in this example). You have to recall that a negative number times another negative number will lead to a positive result, so you can’t have two negatives (since you need to find two numbers that multiply together to make -40).

Eventually, after some trial-and-error, you should find that -8 and +5 satisfy both conditions:

  • -8 + 5 =-3 (the value of b) ✓

  • -8 x 5 = -40 (the value of c) ✓

Step Three: Use your numbers from step two to write out the factors

Finally, you can conclude that the factors of x² - 3x -40 are (x-8) and (x+5).

(You make sure that this answer is correct, you can perform double distribution on (x-8)(x+5) to make sure that the result is equal to the original trinomial).

 

Figure 09: The factors of x² - 3x -40 are (x-8) and (x+5).

 

If you want more practice factoring trinomials when a=1, check out our free step-by-step guide on how to factor trinomials to gain some more practice.

And if you want more independent practice opportunities, check out our free Factoring Polynomials Worksheet Library, where you can download free PDF practice worksheets with answer keys.

Otherwise, you can continue on to learn how to factor polynomials with 3 terms when a≠1.

How to Factor Polynomials with 3 Terms when a≠1

Example #1: Factor 2x² - x - 6

For the first example, we have to factor the trinomial: 2x² - x - 6

 

Figure 10: How to factor polynomials with 3 terms when a≠1

 

For starters, notice that you can not pull out a GCF.

So, to solve trinomials of the form ax² + bx + c when a≠1, you can use the AC method as follows:

Step One: Identify the values of a and c and multiply them together

In this case, a=2 and c=-6, so

  • a x c = 2 x -6 = -12

Step Two: Factor and replace the middle term

The second step requires you to use the result from step one to factor and replace the middle term.

The middle term is currently -1x and note that:

  • -12 = -4 x 3; and

  • -4 + 3 = -1

We chose -4 and 3 as factors because the sum of -4 and 3 equals negative 1, so we can rewrite the original trinomial as 2x² - 4x +3x - 6

 

Figure 11: Factor and replace the middle term

 

Step Three: Split the new polynomial down the middle and take the GCF of each side

Note that we are now working with a polynomial that actually has four terms: 2x² - 4x + 3x - 6

In this third step, you have to split the polynomial down the middle to essentially create two separate binomials that you can simplify by dividing GCF’s out of as follows:

  • First Half: 2x² - 4x = 2x(x-2)

  • Second Half: 3x - 6 = 3(x-2)

This third step is illustrated in Figure 12 below:

 

Figure 12: Split the new polynomial down the middle and take the GCF of each side

 

Step Four: Identify the Factors

Finally, you are ready to identify the factors.

The result from the previous step was 2x(x - 2) + 3(x -2). Hidden within this expression are your two factors, which you can see by looking at Figure 13 below.

 

Figure 13: The final step is to identify the factors

 

Finally, you can conclude that the factors of 2x² - x - 6 are (2x+3) and (x-2).

Clearly, factoring a trinomial when a≠1 can be a tricky and there are several steps along the way, but, the more that you practice this process, the better you will become at factoring polynomials with 3 terms like the one in this past example. To give you a little more practice, lets work through one more example before we move on to learning how to factor cubic polynomials.

Example #2: Factor 4x² - 15x + 9

 

Figure 14: Factor the trinomial where a=4, b=-15, and c=9

 

Step One: Identify the values of a and c and multiply them together

In this example, a=4 and c=9, so

  • a x c = 4 x 9 = 36

Step Two: Factor and replace the middle term

For the next step, note that the middle term is -15x, so you will need to find two numbers that multiply to 36 and add to -15:

  • 36 = -12 x -3; and

  • -12 + -3 = -15

Now, we can rewrite the original trinomial as 4x² -12x -3x +9

Step Three: Split the new polynomial down the middle and take the GCF of each side

For step three, you have to split the polynomial into two separate binomials and divide a GCF out of each one as follows:

  • First Half: 4x² -12x = 4x(x-3)

  • Second Half: -3x+9 -3(x-3)

Step Four: Identify the Factors

The last step is to identify the factors as shown in Figure 15 below.

 

Figure 15: The factors are (4x-3)(x-3)

 

Now, you can conclude that the factors of 4x² - 15x + 9 are (4x-3) and (x-3).

You can again use double distribution on (4x-3)(x-3) to verify that your solution is correct.

If you need more step-by-step help with how to factor polynomials with 3 terms when a does not equal 1, visit out our free Factoring Polynomials Worksheet Library, where you can download free PDF practice worksheets with answer keys.

Otherwise, continue on to the final section where you will learn how to factor polynomials with 4 terms.

How to Factor Polynomials with 4 Terms

The last section of this guide will cover how to factor polynomials with 4 terms and how to factor cubic polynomials.

In this section, we are going to apply a grouping method for how to factor a cubic polynomial that is very similar to the way that you factored trinomials when the leading coefficient, a, did not equal one in the last section. So, you may want to review that section before moving onto the 4 term polynomial factoring examples, however, it is not completely necessary, as we will be taking a step-by-step approach to solving two examples of factoring cubic polynomials.

Now, lets go ahead and work through our first example on how to factor cubic polynomials.

 

Figure 16: Polynomials with 4 terms are referred to as cubic polynomials.

 

Example #1: Factor 2x³ - 3x² + 18x - 27

For the first example, we have to factor the cubic polynomial: 2x³ - 3x² + 18x - 27

Step One: Split the cubic polynomial into groups of two binomials.

To factor this 4 term polynomial, we are going to apply what is called the grouping method, which requires you to split the polynomial into two groups (two separate binomials) with the goal of factoring a GCF out of each one.

 

Figure 17: How to Factor Cubic Polynomials by Grouping: The first step is to split the polynomial into two groups of binomials.

 

Remember that the goal is to create two separate binomials that have a GCF. If there is no apparent GCF, you have the option of swapping the positions of the middle terms (- 3x² and 18x), but that is not necessary for factoring this 4 term polynomial.

In this example, by the end of step one, you now have two groups to factor:

  • (2x³ - 3x²)

  • (18x - 27)

Step Two: Factor each binomial by pulling out a GCF

Now, go ahead and divide a GCF out of each binomial as follows:

  • (2x³ - 3x²) → x²(2x - 3)

  • (18x - 27) → 9(2x - 3)

This step is illustrated in Figure 18 below.

 

Figure 18: How to factor a cubic polynomial by grouping.

 

Step Three: Identify the factors

Notice that both results have a (2x-3) term. This is important and expected. If both results do not share a same term, then you either made a mistake or the polynomial with 4 terms is not factorable.

But, since we were able to factor each group by pulling out a GCF that resulted in both groups sharing a common factor of (2x-3), we know that we can factor out the other terms (x² and +9), so now have our factors: (x²+9) and (2x-3)

Final Answer: The factors of 2x³ - 3x² + 18x - 27 are (x²+9) and (2x-3)

The entire process of how to factor polynomials by 4 terms by grouping is illustrated in Figure 19 below.

 

Figure 19: The factors of 2x³ - 3x² + 18x - 27 are (x²+9) and (2x-3)

 

Example #2: Factor 3y³ + 18y² + y + 6

Let’s gain some more practice with how to factor a cubic polynomial by grouping by solving one more example problem.

In this case, we have to factor the cubic polynomial 3y³ + 18y² + y + 6 using the same grouping method as the previous example.

Step One: Split the cubic polynomial into groups of two binomials.

Start by splitting the cubic polynomial into two groups (two separate binomials).

 

Figure 20: Split the cubic polynomial into two groups of binomials and check to see if they can both be factored by pulling out a GCF.

 

As shown in Figure 20 above, by completing step one, you are left with these two groups

  • (3y³ +18y²)

  • (y+6)

Hold on! Before moving onto the next step, you should notice that the second group (y+6) cannot be factored by pulling out a GCF (because there is no greatest common factor between 1y and 6).

However, notice that we can swap the middle terms of the cubic polynomial (18y² and +y) as shown in Figure 21 below.

Now, we can factor a new 4 term polynomial 3y³ + y + 18y² + 6 that is equivalent to the original 4 term polynomial since the commutative property of addition allows you to rearrange the terms.

 

Figure 21: The commutative property of addition allows you to rearrange the middle terms when you are unable to group and GCF the original cubic polynomial.

 

Notice that you can split this new polynomial into two binomials that can be factored by pulling out a GCF:

  • (3y³ + y)

  • (18y² + 6)

 

Figure 22: After rearranging the original cubic polynomial, you can split it into two binomial groups that can be factoring by pulling out a GCF.

 

Step Two: Factor each binomial by pulling out a GCF

As illustrated in Figure 22 above, after rearranging the original cubic polynomial, you can split it into two binomial groups that can be factoring by pulling out a GCF as follows:

  • (3y³ + y) → y(3y² + 1)

  • (18y² + 6) → 6(3y² + 1)

Step Three: Identify the factors

Now, you can see that both factors have a (3y² + 1) term, which means that you have factored correctly.

Final Answer: The factors of 3y³ + 18y² + y + 6 are (y+6) and (3y² + 1)

The entire process of how to factor polynomials a cubic polynomial like the one in this example is illustrated in Figure 23 below.

 

Figure 23: How to factor cubic polynomials by grouping (step-by-step).

 

Factoring Polynomials Advanced Problems

Now that we have covered how to factor polynomials in a variety of different ways, let’s take a look at two advanced factoring polynomials problems. These are the type of questions that you might find on a unit test or a standardized exam. Let’s see if we can apply what we learned earlier in this guide to solve it.

Advanced Factoring Polynomials Problem #1

Factor: (2/3)x² + (1/3)x -1

At first glance, this factoring problem looks different than our previous examples because it has fractions as coefficients. However, since the polynomial is in ax² +bx + c form, we can factor it using a familiar strategy.

First, let’s identify the values of a, b, and c:

  • a= 2/3

  • b=1/3

  • c=-1

Since 2/3, 1/3, and 1 do not share any common factors, we can not pull out a GCF.

Figure 24: Factoring Polynomials Advanced Problem #1

But, we can use the AC method to factor this trinomial as follows:

Step One: Identify the values of a and c and multiply them together

In this case, a=2/3 and c= -1, so

  • a x c = 2/3 x -1 = (-2/3)x

Step Two: Factor and replace the middle term

For the next step, we have to use our result from step one to factor and replace the middle term (1/3)x:

The middle term is currently -1x and note that:

  • (1/3)x = (-2/3)x + 1x

Since our current middle term ((1/3)x is equivalent to (-2/3)x + 1x, we can rewrite the original trinomial as:

  • (2/3)x² - (2/3)x + 1x -1

Step Three: Split the new polynomial down the middle and take the GCF of each side

For the third step in the AC method, we have to split the polynomial down the middle and take the GCF of each side:

  • First Half: (2/3)x² - (2/3)x

  • Second Half: 1x -1

After taking out the GCF, we are left with:

  • First Half: (2/3)x² - (2/3)x → (2/3)x(x-1)

  • Second Half: 1x -1 → +1(x-1)

Step Four: Identify the Factors

Finally, you just have to identify the factors, which are ((2/3)x+1)(x-1)

Final Answer: (2/3)x² + (1/3)x -1 = ((2/3)x+1)(x-1)

The entire step-by-step process for solving this problem is shown in Figure 24.

 

Advanced Factoring Polynomials Problem #2

Factor: x³ -3x² -4x + 12

We can factor this cubic polynomial by grouping:

  • (x³ -3x²) + (-4x + 12)

Next, we have to factor each separate group:

  • (x³ -3x²) → x²(x-3)

  • (-4x + 12) → -4(x-3)

Now, we can factor out (x-3), and rewrite the result as:

  • (x²-4)(x-3)

While this may look like a final answer, we should notice that (x²-4) is a difference of two squares that we can factor as:

  • (x²-4) = (x+2)(x-2)

Finally, we can conclude that:

Final Answer: x³ -3x² -4x + 12 = (x-3)(x+2)(x-2)

Free Factoring Polynomials Practice Worksheets

If you want to further test your understanding of factoring polynomials, including the difference of two squares, factoring trinomials, factoring by completing the square, and factoring polynomials by grouping, then visit the Mashup Math Factoring Polynomials Worksheet Library, where you can download several free PDF practice worksheets with complete answer keys.

Click here to access our free Factoring Polynomials Worksheet Library.

How to Factor Polynomials: Conclusion

Learning how to factor a polynomial is an important algebra skill that every math student must learn at some point.

While factoring polynomials can be tricky, there are several useful and effective strategies that you can use to factor polynomials. The strategy that you choose will depend on how many terms a polynomial has (as you will often be dealing with factoring polynomials with 2, 3, or 4 terms).

The best way to get better at factoring polynomials (especially cubic polynomials that have 4 terms) is by working through practice problems step-by-step. If you feel like you need more practice, we highly recommend working through the examples in this guide several times to gain more experience.

Keep Learning:

3rd Grade Word Problems—Free PDF Worksheet Library

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3rd Grade Word Problems—Free PDF Worksheet Library

3rd Grade Word Problems—Free PDF Worksheets with Answer Keys

Looking for Free Printable 3rd Grade Math Worksheets?

 

Are you looking for free and engaging 3rd grade math word problems worksheets to share with your students?

 

Whether you are a 3rd grade classroom teacher or a parent of a 3rd grade student, you could use some free and engaging word problems for 3rd grade students to help them to develop important foundational math skills. This page shares a huge collection of 3rd grade word problems that cover topics including addition, subtraction, two-step problems, elapsed time, and more.

Jump to a Topic:

Whether you’re in need of worksheets for addition or subtraction word problems, two-step word problems for 3rd grade students, telling time and elapsed time word problems, area and perimeter word problems, or even measurement word problems, the 3rd grade word problems worksheet collection below will surely have something for you.

 

All of our 3rd grade math word problems worksheets are easy to print and share in your classroom.

 

3rd Grade Word Problems: Single-Digit Addition

▶ Math Skill Focus: Simple Addition, Adding Single-Digit Numbers

The following 3rd Grade Word Problems focus on basic addition in real-world scenarios.

You can preview any of the worksheets in this collection by clicking on any of the image boxes below, and you can download the corresponding PDF file by clicking on any of the blue text links. Each PDF file will include a set of word problems for 3rd grade students followed by a complete answer key on the last page.

For example, Dotty made 2 sugar cookies and 7 chocolate chip cookies. How many cookies did she make in total?

Worksheet A

Worksheet B

Worksheet C

These 3rd grade word problems worksheets focus on the basic foundational skill of adding single-digit numbers in a real-world context. They require students to identify key information, use mathematical thinking, correctly perform simple addition, and express their answer in writing.

3rd Grade Word Problems: Double-Digit Addition

▶ Math Skill Focus: Simple Addition, Adding Double-Digit Numbers

Once your students have mastered solving single-digit word problems for 3rd grade, the next step is to work through similar problems that involve adding two-digit numbers to solve word problems related to real-world scenarios.

For example, Elly is making donuts to sell at a local bake sale. He bakes 24 chocolate donuts, 21 vanilla donuts, and 15 cinnamon donuts. How many donuts did Elly bake?

Worksheet A

Worksheet B

Worksheet C

Do you want more free 3rd Grade Math Activities in your inbox every week?

 
 

3rd Grade Word Problems: Single-Digit Subtraction

▶ Math Skill Focus: Simple Subtraction, Subtracting Single-Digit Numbers

The following 3rd Grade Word Problems focus on basic subtraction in real-world scenarios. Once students have mastered these types of 3rd grade math word problems, they can move onto the double-digit subtraction word problems in the next section.

For example, Ruben planted 12 flower seeds in his garden. After the first week, 3 of the seeds sprouted. After the second week, 5 more of the seeds sprouted. How may of the seeds did not sprout?

Worksheet A

Worksheet B

Worksheet C

3rd Grade Word Problems: Double-Digit Subtraction

▶ Math Skill Focus: Simple Subtraction, Subtracting Double-Digit Numbers

Once your students are comfortable with solving 3rd grade math word problems involving single-digit subtraction, they can take the next step to solving problems involving finding the difference of two-digit numbers in a word problem format.

For example, Bethany has to cleanup after a dinner party. She has to wash 28 dishes in total. She has already washed 12 of the dishes. How many dishes does she have left to wash?

Worksheet A

Worksheet B

Worksheet C

In the next section, we will share some word problems for 3rd grade that focus on mixed addition and subtraction, where students will have to extend their thinking to using the context clues from each problem to determine whether they have to perform addition or subtraction to solve each problem.

3rd Grade Word Problems: Mixed Addition and Subtraction

▶ Math Skill Focus: Mixed Addition and Subtraction, Word Problem Solving

This next set of 3rd grade math word problems require students to use their math skills to determine whether or not they have to use addition or subtraction to solve each word problem.

For example, There were 24 notebooks in a bin. Students took 11 for their backpacks. How many notebooks are left in the bin?

3rd Grade Word Problems: Two-Step Word Problems

▶ Math Skill Focus: Use addition and/or subtraction to solve two-step word problems

One of the biggest differences between 2nd grade math and 3rd grade math is that 3rd graders begin learning how to solve word problems that require multiple steps to solve.

For example, Joey has 10 apples. He gives 4 apples to Josh and 3 apples to Jane. How many apples does Joey have left?

Worksheet A

Worksheet B

Worksheet C

The next two sections will share word problems for 3rd grade students that focus on two auxiliary topics: elapsed time and area and perimeter of rectangles.

3rd Grade Word Problems: Elapsed Time

▶ Math Skill Focus: Solve word problems involving time, units of time (minutes, hours, etc.), and elapsed time

Outside of learning how to solve word problems involving operations, another important 3rd grade math topic is dealing with time, units of time, and elapsed time. This section shares three 3rd grade word problems worksheets related to elapsed time.

For example, Jackson started his homework at 3:15 PM. He finished at 3:50 PM. How many minutes did he spend on completing his homework?

Worksheet A

Worksheet B

Worksheet C

3rd Grade Word Problems: Area and Perimeter of Rectangles

▶ Math Skill Focus: Solve word problems involving area and perimeter of rectangles

This final section includes 3rd grade math word problems worksheets on finding the area and/or perimeter of rectangular figures in real-world scenarios.

For example, Aaron is building a small rectangular flower box that is 5 feet long and 3 feet wide. What is the area, in square feet, of Aaron’s flower box?

Note that Worksheet A focuses on area only, Worksheet focuses on perimeter only, and Worksheet C involved mixed area and perimeter 3rd grade math word problems.

Worksheet A

Worksheet B

Worksheet C

Looking for More 3rd Grade Practice Worksheets?

Be sure to visit our Free 3rd Grade Math Worksheet Library, which shares hundreds of free PDF practice worksheets for a variety of 3rd grade topics.

Helpful Hints for Solving 3rd Grade Math Word Problems

The focus of our 3rd grade word problems worksheets is to give early elementary students to apply their procedural math skills to real-world situations and scenarios. Rather than just asking students to solve a simple math operation problem (e.g. 9 + 7 = ?), these types of problems are more advanced, as they require students to apply reading comprehension and to use context clues to find answers.

Since math word problems are more advanced, many students will initially struggle with them, and it takes time and practice to get better at solving 3rd grade word problems (one-step or two-step) whether they involve addition, subtraction, multiplication, mixed operations, elapsed time, or area and perimeter.

If your 3rd grader is having a hard time with solving any of the problems on any of our 3rd grade word problems worksheets, here are a few helpful hints to improve their chances of correctly solving any given word problem:

  • Read Each Question Carefully: One of the biggest reasons why 3rd graders struggle with word problems is because they fail to read each question carefully and correctly assess exactly what the problem is asking them to do. Before students attempt to solve a math word problem, they need to read to problem, identify and keywords or important information, and identify exactly what the question is asking them to do. Many students will benefit greatly from using a marker to underline key information or by using a colored highlighter.

  • Ask Questions Before You Start: While this advice applies to solving any math problem, it is particularly useful whenever students are working on math word problems. Once you have carefully read a question and identify the important information, you should ask yourself “what is this question asking me to do?” and “what will the final answer look like?”. These two questions help students come up with a plan before they attempt to solve a problem. For example, if a question asks students to find the area of a rectangle, they should be aware that their final answer will have to be in terms of square units.

Helpful Hints for Solving 3rd Grade Word Problems: Always show your work and answer using complete sentences.

  • Show Your Work: All of our 3rd grade word problems worksheets require students to show their work. But, what does showing your work actually look like? In addition to students writing out how they performed their operations, they should also be encouraged to use additional visual aids such as drawing diagrams or using tally marks. For example, when solving an area of a rectangle word problem, it is incredibly helpful to draw a rectangle and label the length of each side before attempting to solve the problem. Or, if a question involves combining a pile of 13 apples with a pile of 9 apples, students can draw each pile and then count the total number of apples.

  • Write Your Final Answer in Sentence Form: In math, word problems typically have “word answers”, so students should get used to expressing their final answer to any word problem by using a complete sentence. While this is a general rule, it is good practice for students. For example, when solving the problem “Ethan read 32 pages on Monday and 21 pages on Tuesday. He wants to read 120 pages this week. How many more pages does he need to read? “, the final answer is not just 67, but “Ethan needs to read 67 more pages.”

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53 Funny Teacher Memes to Brighten Your Day!

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53 Funny Teacher Memes to Brighten Your Day!

53 Funny Teacher Memes Every Educator Can Relate To

Get Ready to Laugh Out Loud with These Funny Memes About Teaching!

Ready for Some Funny Teacher Memes?

Being a teacher is one of the toughest—and often most under-appreciated—careers a person can have.

And, while teaching can be an incredibly rewarding job with tons of positives (like making a difference in the daily lives of your students), there are also some negatives and frustrations that accompany the task of educating students for a living.

In the spirit of taking the bad with the good when it comes to be a teacher, it can fun be to celebrate the quirks of the profession, many of which only yourself and fellow teachers can truly understand.

So, let’s take a moment to celebrate the craft that is being a professional educator in a fun and humorous way by sharing the best and funniest teacher memes that the internet has to offer!

Below you will find our collection of the 53 best teacher memes, many of which are all too relatable to those who work inside of a classroom. Each teacher meme shines a light on some of the more frustrating and/or perplexing aspects of being a teacher at any grade level.

Whether you are dealing with rowdy children, out-of-touch administrators, delusional parents, or never-ending meetings and conferences that obviously could have been emails, this page surely has a meme or two that will have you rolling on the floor laughing in no time!

A hysterical teacher meme or two is just what you need to make it through your day!

Before you jump into our collection of 53 funny teacher memes, remember that each teach meme is meant to be playful and they are meant to be taken light-heartedly. Also remember that laughter is often the best medicine and it’s totally fine to laugh out loud at some of the vexing aspects of being an educator.

Whenever you are ready to laugh, scroll down to start enjoying our funny teacher memes and, if you find any memes to be exceptionally hysterical, then feel free to share this page with your fellow teachers to spread some much-needed joy and laughter :)

Funny Teacher Memes #1-10

1.) This can happen to the best of us.

 

Teacher Meme #1: When you forget to remember…

 

2.) I swear, I was only gone for two seconds!

 

Teacher Meme #2: 😬

 

3.) When the classroom telephone starts ringing the tenth time today…

 
 

4.) Yes, yessssss….

 

This may be the best teacher meme of all time!

 

5.) Your students doing anything to avoid actually doing their classwork…

 

Funny Teacher Meme via Reddit User u/aRabidGorilla

 

6.) All of the moisturizer in the world couldn’t save us!

 

Teaching Memes Every Educator Can Relate To!

 

7.) Is this even written in English?

 

Funny Teacher Memes #7

 

8.) Your reaction to accidentally overhearig your students’ personal conversations…

 
 

9.) You can not possibly be even remotely serious…

 

Teaching Memes #10

 

10.) When you’re in the middle of an awesome lesson and the fire alarm goes off…

 
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Funny Teacher Memes #11-20

Are you ready for the next ten hysterical teacher memes that will have you and your colleagues laughing out loud?

11.) We’re all thinking it…

 

Funny Memes About Teaching: What does the principle even do?

 

12.) When you start handing out rulers to your students…

 
 

13.) It’s sad—I mean, funny—because it’s true.

 

Teacher Memes: Sad, but True.

 

14.) May I laugh at this funny teacher meme?

 

Funny Teacher Memes #14

 

15.) You shall not pass!

 

Teacher Meme #11

 

16.) Good riddance!

 

Funny Teacher Memes #16

 

17.) When April Fools’ Day falls on the weekend….

 
 

18.) Dream on, dreamers…

 
 

19.) We actually just sat around and waited….

 

This teacher meme hits hard!

 

20.) If looks could kill…

 

53 Best Teacher Memes #20: Always show your work!

 

Funny Teacher Memes #21-30

Let’s keep the good times going with our next ten funny teacher memes!

21.) Every day is important!

 

Funny Teacher Memes #21

 

22.) Is anyone even listening to me?

 

My favorite teacher meme of all time!

 

23.) When you find out that you have to waste your off period sitting through another meeting…

 
 

24.) Just smile and nod…smile and nod…

 

Teacher Meme #24: Is this relatable to you?

 

25.) Some say that she’s still waiting…

 

Funny Teacher Memes

 

26.) This one is all too real!

 

Funny Memes About Teaching!

 

27.) Just gotta’ keep on truckin’…

 

This teacher meme is a little too real, isn’t it?

 

28.) When the copy machine is broken again…

 
 

29.) How sweet it is!

 

Funny Teacher Meme #29: Gotta savor the good stuff!

 

30.) When a student asks you how old you are…

 
 

Funny Teacher Memes #31-40

And now for ten more funny memes teacher edition.

31.) Let me just rest my eyes for a quick second…

 

Funny Teacher Memes: Teachers at home at 7:38pm…

 

32.) When a past student tells you that you were their favorite teacher…

 
 

33.) There can only be one…

 

Teacher Memes #33: The Teacher’s Dilemma.

 

34.) You couldn’t use the telephone and go on the internet at the same time!

 
 

35.) When a student’s math homework is written in pen…

 
 

36.) Wink, wink…

 

This is my favorite teacher meme of all time!

 

37.) Whatchu’ want me to say?

 

Teacher Meme #37: This one is spicy, we know!

 

38.) Back in my day….

 

Funny Teacher Memes #38

 

39.) Don’t pop the Champagne too early!

 

I have this teacher meme posted in my classroom!

 

40.) When you get an email telling you that your after-schooling meeting was cancelled…

 
 

Funny Teacher Memes #41-53

Our funny teacher memes collection wraps up with 13 more super funny teacher memes that will have your sides hurting!

41.) Feelin’ hot, hot, hot!

 

Can you relate to this funny teacher meme?

 

42.) Ya gotta’ love it!

 

Funny Teacher Memes #42

 

43.) When your class gets interrupted by a knock at the door…

 
 

44.) I guess it just doesn’t work that way…

 
 

45.) When you already explained something five different ways and students are still saying that they don’t get it…

 
 

46.) It takes two to Tango….

 

I also have this teacher meme posted in my classroom.

 

47.) When you find out that your students were well-behaved for the sub…

 
 

48.) If only a Panera Bread platter could solve all of our problems…

 

Is teacher meme #48 a truth bomb?

 

49.) No, I will not cover hall duty right now…

 
 

50.) The Parent-Teacher Conference Day experience in a nutshell…

 
 

51.) Most of us will probably go this way…

 
 

52) I’m not crying, you’re crying!

 

Funny Teacher Meme #52

 

53.) Every teacher after the last day of school before summer vacation…

 
 

That wraps up our list of the 53 funniest teacher memes that the internet has to offer! We hope that you these memes brightened up your day, and that you had a few laughs along the way. If you are looking for a few different ways that you can share and enjoy these teacher memes, here are a few ideas:

  • Revisit this page whenever the demands of teaching are weighing you down and you need a good chuckle or two to restore your sanity.

  • Share your favorite teacher memes in your teacher group chat or email chain to indulge in some humorous commiseration!

  • Post a funny teacher meme on social media to connect with fellow teachers, parents, and administrators.

  • Print and post a few funny teacher memes in your classroom to share some insight and humor with your students. This can be a fun way to give your students an idea of some of the challenges of being a teacher and working with students for a living.

  • Use these memes in meeting and/or professional development presentations to serve as an icebreaker or to simply break things up by injectiing some light-hearted and topical humor into the mix.

(Do you want more free K-8 math resources and activities in your inbox every week? Click here to sign up for our math education email newsletter)

Did you laugh, cry, or both? Share your reaction in the comments below!

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