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
Factoring out the Greatest Common Factor (GCF) Test:
#1:
Instructions: Factor out the Greatest Common Factor (GCF).
a) -7b^{2} - 56b^{4}
b) -20n + 10
#2:
Instructions: Factor out the Greatest Common Factor (GCF).
a) 28xy + 49x + 56
b) -90x^{3} - 81xy + 18x^{2}
#3:
Instructions: Factor out the Greatest Common Factor (GCF).
a) 12x^{2}y + 32y - 4x
b) 10x^{2}y^{4} + 10x^{2}y^{3} + 20xy^{3}
#4:
Instructions: Factor out the Greatest Common Factor (GCF).
a) (8x^{3} - 3x^{2} + 1)(2x^{7} - 5) + (2x^{7} - 5)(11x - 1)
#5:
Instructions: Factor out the Greatest Common Factor (GCF).
a) (6x + 13)(-2x^{3} - 8) - (3x^{3} - 12)(6x + 13)
Written Solutions:
Solution:
a) -7b^{2}(1 + 8b^{2})
b) 10(-2n + 1)
Solution:
a) 7(4xy + 7x + 8)
b) -9x(10x^{2} + 9y - 2x)
Solution:
a) 4(3x^{2}y + 8y - x)
b) 10xy^{3}(xy + x + 2)
Solution:
a) x(2x^{7} - 5)(8x^{2} - 3x + 11)
Solution:
a) (6x + 13)(-5x^{3} + 4)