(7) Lesson 5.8 - Factor Linear Expressions

1. Subtract. Use models if needed.
1. (5x + 5) - (2x - 4)
2. (-3x - 4) - (3x + 3)
3. (7x - 6) - (x - 3)
4. (-3x + 3) - (-5x - 3)
5. The perimeter of the triangle is
13x - 1. What is the measure of
the missing side?
Course 2, Lesson 5-8

2. ANSWERS
1. 3x + 9
2. –6x – 7
3. 6x – 3
4. 2x + 6
5. 7x – 3
Course 2, Lesson 5-8

3. HOW can you use numbers and
symbols to represent mathematical
ideas?
Expressions and Equations
Course 2, Lesson 5-8

4. • 7.EE.1
Apply properties of operations as strategies to add, subtract, factor,
and expand linear expressions with rational coefficients.
• 7.EE.2
Understand that rewriting an expression in different forms in a
problem context can shed light on the problem and how the quantities
in it are related.
Course 2, Lesson 5-8 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Expressions and Equations

5. Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
Course 2, Lesson 5-8 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Expressions and Equations

6. • To find the GCF of monomials
• To factor linear expressions
Course 2, Lesson 5-8
Expressions and Equations

7. • monomial
• factor
• factored form
Course 2, Lesson 5-8
Expressions and Equations

8. 1
Need Another Example?
2
Step-by-Step Example
1. Find the GCF of the pair of monomials.
The GCF of 4x and 12x is 2 • 2 • x or 4x.
Write the prime factorization of 4x and 12x.4x = 2 • 2 • x
4x, 12x
12x = 2 • 2 • 3 • x Circle the common factors.

9. Answer
Need Another Example?
Find the GCF of 48x and 28x.
4x

10. 1
Need Another Example?
2
Step-by-Step Example
2. Find the GCF of the pair of monomials.
The GCF of 18a and 20ab is 2 • a or 2a.
Write the prime factorization of 18a and 20ab.18a = 2 • 3 • 3 • a
18a, 20ab
20ab = 2 • 2 • 5 • a • b Circle the common factors.

11. Answer
Need Another Example?
Find the GCF of 16s and 40st.
8s

12. 1
Need Another Example?
2
Step-by-Step Example
3. Find the GCF of the pair of monomials.
The GCF of 12cd and 36cd is 2 • 2 • 3 • c • d or 12cd.
Write the prime factorization of 12cd and 36cd.12cd = 2 • 2 • 3 • c • d
12cd, 36cd
36cd = 2 • 2 • 3 • 3 • c • d Circle the common factors.

13. Answer
Need Another Example?
Find the GCF of 14ab and 28ab.
14ab

14. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
4. Factor 3x + 9.
The GCF of 3x and 9 is 3. Write each term as a product of the
GCF and its remaining factors.
Write the prime factorization of 3x and 9.3x = 3 • x
9 = 3 • 3 Circle the common factors.
Use a model.
x + 3
3
Arrange three x-tiles and nine 1-tiles into equal
rows and columns. The rectangle has a width of
three 1-tiles, or 3, and a length of one x-tile and
three 1-tiles, or x + 3.
Use the GCF.
3x + 9 = 3(x) + 3(3)
= 3(x + 3) Distributive Property
So, 3x + 9 = 3(x + 3).

15. Answer
Need Another Example?
Factor 12x + 48.
12(x + 4)

16. 1
Need Another Example?
2
3
Step-by-Step Example
5. Factor 12x + 7y.
There are no common factors, so 12x + 7y cannot be factored.
Find the GCF of 12x and 7y.
7y = 1 • 7 • y
12x = 2 • 2 • 3 • x

17. Answer
Need Another Example?
Factor 3x + 11.
cannot be factored

18. 1
Need Another Example?
2
3
4
Step-by-Step Example
6. The drawing of the garden at
the right has a total area of
(15x + 18) square feet. Find
possible dimensions of the
garden.
The GCF of 15x and 18 is 3. Write each term as a product
of the GCF and its remaining factors.
Factor 15x + 18.
18 = 2 • 3 • 3
15x = 3 • 5 • x Write the prime factorization of 15x and 18.
Circle the common factors.
15x 18
= 3(5x + 6)
15x + 18 = 3(5x) + 3(6)
Distributive Property
So, the possible dimensions are 3 feet by (5x + 6) feet.

19. Answer
Need Another Example?
Lily’s favorite picture has an area of (3x + 12)
square inches. Find possible dimensions of
the picture.
3 in. by (x + 4) in.

20. How did what you learned
today help you answer the
HOW can you use numbers and symbols
to represent mathematical ideas?
Course 2, Lesson 5-8
Expressions and Equations

21. How did what you learned
today help you answer the
HOW can you use numbers and symbols
to represent mathematical ideas?
Course 2, Lesson 5-8
Expressions and Equations
Sample answers:
• By factoring linear expressions using algebra tiles
• By using factored expressions to represent real-world
situations, like a monthly income and the area of a
dance floor

22. Explain how to factor
54x + 18 using the GCF.
Ratios and Proportional RelationshipsExpressions and Equations
Course 2, Lesson 5-8