Lesson 2
RCSD Geometry Local MATHEMATICS CURRICULUM
U5
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Lesson 2: Factoring Polynomials by GCF
Learning Target

I can Factor an expression using the greatest common factor.( GCF)
Previously, you have simplified expressions by distributing through parentheses, such as:
2(x + 3) = ________________ =___________________
What does it mean to FACTOR? Simple factoring in the context of polynomial expressions is backwards from
distributing. Instead of multiplying something through parentheses, you will be seeing what you can take back
out and put in front of a parentheses, such as:
2x + 6 = __(x) + ___(3) = ___(x + ___)
THE TWO MEANINGS OF FACTOR
1. Factor (verb): To rewrite an algebraic expression as an equivalent product.
2. Factor (noun): An algebraic expression that is one part of a larger factored expression
Finding a GCF: Greatest Common Factor
Example 1: 𝟏𝟒𝒙𝟐 𝒚 and 𝟐𝟏𝒙𝟓
First determine the GCF of the coefficients
14: (1, 2, 7, 14)
21: (1, 3, 7, 21)
Then find the smallest exponent of each common
variable, or the largest power of the variable that
“goes into”
𝑥2
𝑥5
So the GCF of 𝟏𝟒𝒙𝟐 𝒚 and 𝟐𝟏𝒙𝟓 is
_______________
Lesson 2
RCSD Geometry Local MATHEMATICS CURRICULUM
U5
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Example 2: Factor the expression
Factoring by GCF
3x3 + 27x2 + 9x
Step 1: Find the GCF of all of the expression's terms:
a) look at the coefficients
b) look at the variable(s)
Step 2: Write the GCF on the left of a set of parentheses:
Step 3: Divide each term from the original by the GCF and
write it in the parentheses.
Let’s try Together ~ Factor each by factoring out the Greatest Common Factor:
10𝑎𝑏 + 5𝑎
8x  20
3x 2  9 x  18
4 x 4 y 2  6 xy 3
3𝑔3 ℎ – 9𝑔2 ℎ + 12ℎ
4 x 3  6 x 2  8x
6 x 2 y 3  9 xy 4  18 y 5
15x 8 y 5  9 x 4
Lesson 2
RCSD Geometry Local MATHEMATICS CURRICULUM
U5
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Lesson 2: Factoring Polynomials by GCF
Problem Set
Exercise 1: Factor by GCF. Then check by using the distributive property.
Exercise 2. Rewrite each of the following expressions as the product of two binomials by factoring out a
common binomial factor.
Exercise 3
Lesson 2
RCSD Geometry Local MATHEMATICS CURRICULUM
U5
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Lesson 2: Factoring Polynomials by GCF
Homework
1. Identify the greatest common factor for each of the following sets of monomials.