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Factoring out the GCF Test
About Factoring out the Greatest Common Factor:

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 GCF by placing the GCF outside of a set of parentheses. Inside the parentheses, we divide each term by the GCF to get our new terms.

Test Objectives:

•Demonstrate a general understanding of the meaning of the greatest common factor (GCF)

•Demonstrate the ability to find the greatest common factor (GCF) for a polynomial

•Demonstrate the ability to factor out the greatest common factor (GCF) for a polynomial

Factoring out the Greatest Common Factor (GCF) Test:




#1:


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


a) -2x - 2


b) -20n5 + 15n3


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#2:


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


a) 12n2 - 9


b) 64x3y2 + 8x2y2 + 16y2


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#3:


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


a) -63x5y - 21x3y2 + 28x2


b) 27x5y4 - 3xy + 9x


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#4:


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


a) 72h3j2k2 + 6h3jk2 - 54h2jk2 + 48h2jk


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#5:


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


a) -121x5zy + 33xz3y + 77x2z2 + 22xz


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Written Solutions:




#1:


Solution:


a) 2(-x - 1)


b) 5n3(-4n2 + 3)


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#2:


Solution:


a) 3(4n2 - 3)


b) 8y2(8x3 + x2 + 2)


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#3:


Solution:


a) 7x2(-9x3y - 3xy2 + 4)


b) 3x(9x4y4 - y + 3)


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#4:


Solution:


a) 6h2jk(12hjk + hk - 9k + 8)


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#5:


Solution:


a) 11xz(-11x4y + 3z2y + 7xz + 2)


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