Lesson 5-8: Factoring Linear Expressions

Lesson 5-8: Factoring Linear Expressions

Students will be able to...

• find the GCF of monomials

• factor linear expressions

Vocabulary:

Monomial - an algebraic expression with only one term
Ex: 2x, 42, & xyz
Binomial - an algebraic expression with exactly two terms
Ex: 3x+2, 5x-9, & -x+3
Factor - numbers that can multiply together to get another number
Factored Form - when an expression is written as the product of its factors

Multiple Choice

Which of the following is a monomial?

• 2x + 3
• 3x

• 4 + 2x

• 5x - 2

Multiple Choice

Which of the following is a binomial?

• 2x + y

• abc

• 25z

• 2x - 3y + 5

Yes, they both have an x, so the GCF of 4x & 12x is 4x.

Step 2: Are there any variables they both have?

4 12
1x4 1x12
2x2 2x6
3x4

Step 1: Find the GCF of the numbers

Find the GCF of Monomials
Ex 1: 4x & 12x

Yes, they both have an a, so the GCF of 18a & 20ab is 2a.

Step 2: Are there any variables they both have?

18 20
1x18 1x20
2x9 2x10
3x6 4x5

Step 1: Find the GCF of the numbers

Find the GCF of Monomials
Ex 2: 18a & 20ab

Multiple Choice

Find the GCF of 12 & 28c

• 4
• 4c

• 6
• 16

Multiple Choice

Find the GCF of 25x & 15xy

• 10xy
• 5xy

• 3xy
• 5x

Math Response

Find the GCF of 16a and 40ab

Type answer here

Correct Answer: 8a

Deg^°

Rad

-5(3x) = -15x

-5(-4) = 20


= -15x+20

-5(3x-4)

2(x) = 2x

2(5) = 10


= 2x+10

2(x+5)

Refresh: The Distributive Property

Multiple Choice

What is the simplified version of this expression? $$7\left(5x-1\right)$$  

• $$35x+7$$  

• $$35x-1$$  

• $$35x-7$$  

• $$-35x-7$$  

Match

Match the following each expression with what it would be AFTER you distribute.

• 6(x - 3)

• 6(x + 3)

• -6(x - 3)

• -6(x + 3)

6x - 18

6x + 18

-6x + 18

-6x - 18

• 6x - 18

• 6x + 18

• -6x + 18

• -6x - 18

3x ÷ 3 = 1x = x
9 ÷ 3 = 3

Step 2: Divide each term by the GCF

• GCF of 3 & 9 is 3

• no shared variable

• GCF of 3x & 9 is 3

Step 1: Find the GCF between the two terms

Factor Binomials
Ex 3: 3x+9

Step 3: Write the expression in Factored Form

3x+9 = 3(x+3)

Multiple Choice

Write the following expression in factored form:

8x + 16

• 4(2x + 4)

• 1(8x + 16)

• 8(x + 2)

• It can't be factored.

Multiple Choice

Write the following expression in factored form:

15a + 24

• 3(15a + 24)

• 3(5a + 8)

• 3(5a + 24)

• It can't be factored

Multiple Choice

Write the following expression in factored form:

4x+35

• 4(4x+35)

• 2(2x+17)

• 4(x+9)

• It can't be factored

Multiple Choice

Write the following expression in factored form:

36 - 9x

• 3(12 - 3x)

• 9(4 - x)

• 6(4 - 9x)

• It can't be factored.

Multiple Choice

Write the following in factored form:

14y + 35x

• 1(14x + 35y)

• 7(2x + 5y)

• 7(2y + 5x)

• 1(14y + 35x)

Multiple Choice

Write the following expression in factored form:

-6x + 15y - 12

• 3(-2x + 5y - 4)

• 2(-3x + 7y - 6)

• -6(x + 3y - 2)

• It can't be factored.

Math Response

Write the expression in factored form:

4x-28

Type answer here

Correct Answer: 4\left(x-7\right)

Deg^°

Rad

Math Response

Write the expression in factored form:

3x+33y

Type answer here

Correct Answer: 3\left(x+11y\right)

Deg^°

Rad