NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Factor Linear Expressions
A linear expression is in factored form when it is expressed as the product of its factors.
Example 1
Factor 5x + 10.
Use the GCF to factor the linear expression.
5x = 5 ・ x
Write the prime factorization of 5x and 10.
10 = 5 ・ 2
Circle the common factors.
The GCF of 5x and 10 is 5. Write each term as a product of the GCF and its remaining factors.
5x + 10 = 5(x) + 5(2)
= 5(x + 2)
Distributive Property
So, 5x + 10 = 5(x + 2).
Example 2
Factor 3x + 8.
3x = 3・x
8 = 2・2・2
There are no common factors, so 3x + 8 cannot be factored.
Find the GCF of each pair of monomials.
1. 4st, 12s
2. 11gh, 33g
3. 50j, 75jk
Exercises
Factor each expression. If the expression cannot be factored, write cannot be factored.
4. 15x + 10
5. 6x + 9
6. 13x + 14
7. 24x – 18
8. 16x – 12
9. 130x – 13
Expressions
85
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Homework Practice
Factor Linear Expressions
Find the GCF of each pair of monomials.
1. 20, 45x
2. 30w, 70w
3. 16mn, 24m
4. 50j, 75jk
Factor each expression. If the expression cannot be factored, write cannot be factored.
5. 4x + 12
6. 5x + 35
7. 32x – 15
8. 6x – 9
9. 72 – 18x
10. 100x + 150
25. GEOMETRY The rectangle shown below has a
total area of (4x + 36) square feet. Factor 4x + 36.
26. FUNDRAISING The Art Club receives $10 plus $2
for every sculpture they sell for a fundraiser. The
expression 2x + 10 represents the amount the Art
Club receives if they sell x sculptures.
Factor 2x + 10.
4x
Expressions
36
85