Factoring Expressions

Factoring Expressions

Mrs. Baird 7th Grade

What is Factoring?

Finding the GCF between all terms and "factoring" (dividing it out) of each term. *It is the reverse of the distributive property.

We factor expressions for a few reasons:

1. To easily identify the different variables and terms of the expression.

2. To solve for an unknown variable in fewer steps.

Simplifying an Expression by Factoring

Let's start with this expression:

12a + 24

Simplifying an Expression by Factoring

First, we need to identify the numbers that we will find the GCF of.

12a + 24: the numbers are 12 and 24.

Question 1: What is the GCF of 12 and 24?

Multiple Choice

What is the GCF of 12 and 24?

• 24

• 12

• 6

• 2

Simplifying an Expression by Factoring

Since our GCF is 12, we will divide both numbers by 12 and rewrite our remaining expression.
 $\frac{12a}{12}$  = 1a  and  $\frac{24}{12}$  = 2

We are left with 1a + 2 for our expression.
*Remember we don't need to write the 1 in front!
a + 2

Simplifying an Expression by Factoring

Now that we have our simplified terms, we can't forget how we simplified them!

Always write the GCF in front of the terms!!!!

12(a + 2)

Question 2: Let's practice finding the GCF some more!

Multiple Choice

What is the GCF of 5 and 20?

• 2

• 5

• 4

• 20

Fill in the Blank

What is the GCF of 16 and 36?

Multiple Choice

What is the GCF in this expression?

24x + 30

• 6

• 10

• 8

• 4

Fill in the Blank

What is the GCF in this expression?

15b + 27

Remember...

After finding the GCF, factor it out and rewrite the expression:

3s + 15 = 3(s + 5)

Question 6: Factor out this expression

4x + 8

Multiple Choice

Factor this expression:

4x + 8

• 2(2x + 4)

• 4(4x + 8)

• 4(x + 2)

• 8(x + 1)

Multiple Choice

Factor this expression:

6d - 36

• 6(d + 6)

• 6(d - 6)

• 2(3d - 18)

• It cannot be factored.

Multiple Choice

Factor this expression:

4f + 4g

• 2(2f - 1g)

• 4(f + 4g)

• 2(2f + 2g)

• 4(f + g)

Fill in the Blank

Factor this expression:

5k - 75

Multiple Choice

Factor.

4x - 10y + 18

• 2(2x - 5y + 9)

• 2(x + 5y - 9)

• 2(2x - 2y + 3)

• It cannot be factored.