### 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

#1:

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

a) -7b^{2} - 56b^{4}

b) -20n + 10

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#2:

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

a) 28xy + 49x + 56

b) -90x^{3} - 81xy + 18x^{2}

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#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}

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#4:

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

a) (8x^{3} - 3x^{2} + 1)(2x^{7} - 5) + (2x^{7} - 5)(11x - 1)
(8x^{3} - 3x^{2} + 1)(2x^{7} - 5) +

(2x^{7} - 5)(11x - 1)

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#5:

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

a) (6x + 13)(-2x^{3} - 8) - (3x^{3} - 12)(6x + 13)
(6x + 13)(-2x^{3} - 8) -

(3x^{3} - 12)(6x + 13)

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Written Solutions:

#1:

Solutions:

a) -7b^{2}(1 + 8b^{2})

b) 10(-2n + 1)

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#2:

Solutions:

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

b) -9x(10x^{2} + 9y - 2x)

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#3:

Solutions:

a) 4(3x^{2}y + 8y - x)

b) 10xy^{3}(xy + x + 2)

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#4:

Solutions:

a) x(2x^{7} - 5)(8x^{2} - 3x + 11)

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#5:

Solutions:

a) (6x + 13)(-5x^{3} + 4)