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) $$12x^2y + 32y - 4x$$
b) $$10x^2y^4 + 10x^2y^3 + 20xy^3$$
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#4:
Instructions: Factor out the Greatest Common Factor (GCF).
a) $$(8x^3 - 3x^2 + 1)(2x^7 - 5) + (2x^7 - 5)(11x - 1)$$
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#5:
Instructions: Factor out the Greatest Common Factor (GCF).
a) $$(6x + 13)(-2x^3 - 8) - (3x^3 - 12)(6x + 13)$$
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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) $$4(3x^2y + 8y - x)$$
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) $$(6x + 13)(-5x^3 + 4)$$
