### About Factor out the GCF:

Once we know how to find the greatest common factor (GCF) for a polynomial, the next step is to learn how to factor. We factor out the greatest common factor (GCF) by placing the greatest common factor (GCF) outside of a set of parentheses. Inside the parentheses, we divide each term by the greatest common factor (GCF) to get our new terms.

Test Objectives
• Demonstrate the ability to find the Greatest Common Factor (GCF)
• Demonstrate the ability to factor out the Greatest Common Factor (GCF)
• Demonstrate the ability to check factoring using the distributive property
Factor out the GCF Practice Test:

#1:

Instructions: Factor out the Greatest Common Factor (GCF).

a) -7b2 - 56b4

b) -20n + 10

#2:

Instructions: Factor out the Greatest Common Factor (GCF).

a) 28xy + 49x + 56

b) -90x3 - 81xy + 18x2

#3:

Instructions: Factor out the Greatest Common Factor (GCF).

a) 12x2y + 32y - 4x

b) 10x2y4 + 10x2y3 + 20xy3

#4:

Instructions: Factor out the Greatest Common Factor (GCF).

a) (8x3 - 3x2 + 1)(2x7 - 5) + (2x7 - 5)(11x - 1) (8x3 - 3x2 + 1)(2x7 - 5) +
(2x7 - 5)(11x - 1)

#5:

Instructions: Factor out the Greatest Common Factor (GCF).

a) (6x + 13)(-2x3 - 8) - (3x3 - 12)(6x + 13) (6x + 13)(-2x3 - 8) -
(3x3 - 12)(6x + 13)

Written Solutions:

#1:

Solutions:

a) -7b2(1 + 8b2)

b) 10(-2n + 1)

#2:

Solutions:

a) 7(4xy + 7x + 8)

b) -9x(10x2 + 9y - 2x)

#3:

Solutions:

a) 4(3x2y + 8y - x)

b) 10xy3(xy + x + 2)

#4:

Solutions:

a) x(2x7 - 5)(8x2 - 3x + 11)

#5:

Solutions:

a) (6x + 13)(-5x3 + 4)