Factoring out the GCF – Practice Problems

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To make polynomials easier to work with, factor out the greatest common factor of each term in the polynomial. The GCF may be obvious or more difficult to determine. If the GCF doesn’t jump out at you, you can always factor each term and hunt for the common factors.

Once you find the GCF, what do you do with it? Good question. To answer that question, we must consider the Distributive Property: a(b + c) = ab + ac. See how the a is outside the parentheses and b + c are inside? When you factor out the GCF of a polynomial, put the GCF outside the parentheses and what’s left of the polynomial, inside the parentheses. Doing this is the reverse of the Distributive Property.

To check your work, go the other direction and distribute the GCF across the terms inside the parentheses. Factoring out the GCF of a polynomial by using the reverse of the Distributive Property, will make it easier to calculate the zeros of the polynomial which is also the answer. Finding the zeros of complicated polynomials can be tricky, and you’ll want to learn every trick or tip in the book, so watch this video to get a head start on complicated algebra problems.

Understand the relationship between zeros and factors of polynomials.

CCSS.MATH.CONTENT.HSA.APR.B.2

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Exercises in this Practice Problem
Describe the greatest common factor (GCF).
Determine the greatest common factor.
Find the greatest common factor.
Consider each term and find the greatest common factor.
Determine the greatest common factor for all the terms listed in an expression.
Name the Greatest Common Factor for each given term.