### 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

#1:

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

a) -2x - 2

b) -20n^{5} + 15n^{3}

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#2:

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

a) 12n^{2} - 9

b) 64x^{3}y^{2} + 8x^{2}y^{2} + 16y^{2}

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#3:

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

a) -63x^{5}y - 21x^{3}y^{2} + 28x^{2}

b) 27x^{5}y^{4} - 3xy + 9x

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#4:

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

a) 72h^{3}j^{2}k^{2} + 6h^{3}jk^{2} - 54h^{2}jk^{2} + 48h^{2}jk

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#5:

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

a) -121x^{5}zy + 33xz^{3}y + 77x^{2}z^{2} + 22xz

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Written Solutions:

#1:

Solutions:

a) 2(-x - 1)

b) 5n^{3}(-4n^{2} + 3)

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#2:

Solutions:

a) 3(4n^{2} - 3)

b) 8y^{2}(8x^{3} + x^{2} + 2)

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#3:

Solutions:

a) 7x^{2}(-9x^{3}y - 3xy^{2} + 4)

b) 3x(9x^{4}y^{4} - y + 3)

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#4:

Solutions:

a) 6h^{2}jk(12hjk + hk - 9k + 8)

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#5:

Solutions:

a) 11xz(-11x^{4}y + 3z^{2}y + 7xz + 2)