9.5 Factor Using GCF

Title: 9.5 Using the Distributive Property to Factor

EQ: What are the steps in factoring using the GCF? (Hint: 3 steps)

Multiple Choice

REVIEW: Use the Distributive Property to simplify the expression.

4(3x+2)

• 3x+8

• 12x+8

• 12x+2

• 12x+6

Multiple Choice

REVIEW: Use the Distributive Property to simplify the expression.

- (x - 4)

• x+4

• x-4

• -x-4

• -x+4

Multiple Choice

Is 3 a factor of 21?

• yes

• no

Find the GCF of 12 and 20.

Example:

Steps:

Greatest Common Factor

1. List all of the factors: what 2 numbers multiply to be the number.

2. Find the common factors.

3. Find the GCF - the biggest number they have in common

Multiple Choice

GCF of 16 and 40

• 4

• 8

• 2

• 10

Multiple Choice

What is the GCF of 12 and 30?

• 2

• 4

• 6

• 360

Multiple Choice

What is the GCF of 20 and 36?

• 2

• 4

• 10

• 720

Write the steps and the Ex. GCF with Variables

Steps:

1. Find the GCF of the numbers

2. Look at the exponents and find out what the variables have in common.

​Find the GCF of 36 and 24

Find the GCF of x⁴ and x²

Find the GCF of y² and y

​Example: Find the GCF of 36x⁴y² and 24x²y

Multiple Choice

What is the GCF of $$15y^4\ and\ 25xy^3$$  

• $$5y^3$$  

• $$5xy^3$$  

• $$3xy^3$$  

• $$3y^3$$  

Multiple Choice

What is the GCF of $$12x^2\ and\ 20x$$  

• $$2x$$  

• $$2x^2$$  

• $$4x$$  

• $$4x^2$$  

Multiple Choice

What is the GCF of: 6x²+18x-27?

• 1

• 3

• 6

• -9

Factor using GCF: 12x²​ + 15xy³

Example:

1. Find the GCF

2. Write the GCF out in front

3. Divide everything by the GCF.

4. Whatever is left over stays inside the parentheses.

Steps:

Factoring out a GCF

Multiple Choice

Factor using GCF:

$$2n-4$$  

• 2(n-2)

• 2n - 4

• 4(2n - 0)

• 2n(1-2)

Multiple Choice

Factor using the GCF:

$$2x^2+10x+42$$  

• $$2\left(x^2+5x+21\right)$$

• $$2\left(2x^2+10x+42\right)$$

• $$x^2+5x+21$$  

• $$2x\left(x^2+5x+21\right)$$  

Multiple Choice

Factor using GCF:

$$36x^2+15x$$  

• $$3x\left(12x+5\right)$$  

• $$6x^2\left(6x+2\right)$$  

• $$3x^2\left(12x+5x\right)$$  

Multiple Choice

Factor 7x + 21 using the GCF

• 7(x+3)

• 7x + 3

• 3(x + 7)

• x(7 + 3)

Multiple Choice

Factor:
x² - 5x

• 1(x - 5)

• x(x - 5x)

• x(x - 5)

• x²(1 - 5)

REMEMBER GCFs-Always Check First!

• Step 1 is always look for a GCF to make factoring easier! 

• Check if all the terms have an Variable AND/OR a number you can divide out as the first factor

• As we continue factoring, this will always be the first step of every problem

Poll

After reviewing basic factoring- on a scale of 1 to 4, how do you feel about factoring?

• 4- This is easy, I could teach it to the class

• 3- I am good most of the time

• 2- Ehhh, I can do it some times

• 1- What in the world is this? I wasn't here or coherent when we reviewed this

9.5 Homework

Pg 143 #1-8