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) -7b2 - 56b4
b) -20n + 10
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#2:
Instructions: Factor out the Greatest Common Factor (GCF).
a) 28xy + 49x + 56
b) -90x3 - 81xy + 18x2
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#3:
Instructions: Factor out the Greatest Common Factor (GCF).
a) 12x2y + 32y - 4x
b) 10x2y4 + 10x2y3 + 20xy3
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#4:
Instructions: Factor out the Greatest Common Factor (GCF).
a) (8x3 - 3x2 + 1)(2x7 - 5) + (2x7 - 5)(11x - 1) (8x3 - 3x2 + 1)(2x7 - 5) +
(2x7 - 5)(11x - 1)
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#5:
Instructions: Factor out the Greatest Common Factor (GCF).
a) (6x + 13)(-2x3 - 8) - (3x3 - 12)(6x + 13) (6x + 13)(-2x3 - 8) -
(3x3 - 12)(6x + 13)
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Written Solutions:
#1:
Solutions:
a) -7b2(1 + 8b2)
b) 10(-2n + 1)
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#2:
Solutions:
a) 7(4xy + 7x + 8)
b) -9x(10x2 + 9y - 2x)
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#3:
Solutions:
a) 4(3x2y + 8y - x)
b) 10xy3(xy + x + 2)
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#4:
Solutions:
a) x(2x7 - 5)(8x2 - 3x + 11)
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#5:
Solutions:
a) (6x + 13)(-5x3 + 4)
