About Factoring 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 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 GCF Practice 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:

Solutions:

a) 2(-x - 1)

b) 5n3(-4n2 + 3)

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#2:

Solutions:

a) 3(4n2 - 3)

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

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#3:

Solutions:

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

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

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#4:

Solutions:

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

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#5:

Solutions:

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

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