GCF of Polynomials

Factoring Out GCF in Polynomials

Multiple Choice

What is a factor?

• numbers we can multiply together to get another number

• the total amount resulting from the addition of two or more numbers, amounts, or items

• the action of separating something into parts or the process of being separated

• a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero

​Definitions:

Factor: Factoring is the opposite of distributing. Instead of putting numbers together we are going to take them apart. We will do this by finding out what number divides both of our terms.

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Greatest Common Factor: The greatest common factor is the largest possible number that divides both of the terms.​

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Subject | Subject

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How to Find the Greatest Common Factor (GCF)

The Greatest Common Factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two numbers:

1. List the prime factors of each number.

2. Multiply those factors they both have in common. If there are no common prime factors, the GCF is 1.

GCF continued

Prime Factors of 18: 2 x 3 x 3

Prime Factors of 24: 2 x 2 x 2 x 3

There is one 2 and one 3 in common.

The GCF is 2 x 3 = 6

Example

Find the GCF of 14 and 49

Factors of 14: 2 x 7

Factors 49: 7 x 7

7 is the only common factor.

Therefore the GCF is 7

What about algebraic expressions?

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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

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

Multiple Choice

What is the GCF in this expression?

24x + 30

• 6

• 10

• 8

• 4

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)

​https://youtu.be/Y1Vd5wb0rnM

https://www.youtube.com/watch?v=fEZWqLxViUM

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Time to practice...

Go to page 28 in your book and do exercises 1-12.

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