Explanation Given Information: The polynomial: − 40 x 8 y 6 − 16 x 9 y 5 Concept Used: The GCF (Greatest Common Factor) of a list of integers is the largest integer that is a factor of all the integers in the list. The GCF (Greatest Common Factor) of a list of common variable factors raised to powers is the variable raised to the smallest exponent in the list. Distributive property: a ( b + c ) = a ⋅ b + a ⋅ c To factor out the GCF from the given polynomial, first we rewrite each term of the polynomial as a product of prime factors and identify the largest factor that is common in all terms. Then we factor out the GCF from each term by writing each term as a product of the GCF and the term’s remaining factors inside a parenthesis. The prime factors of the terms − 40 x 8 y 6 , and − 16 x 9 y 5 are shown below: − 40 x 8 y 6 = − 1 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ x 8 y 6 − 16 x 9 y 5 = − 1 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ x 9 y 5 From the above prime factors, we can see that there are fourcommon factorsin all terms, one is − 1 and each ofothers is 2. So the GCF of the numbers would be − 1 ⋅ 2 ⋅ 2 ⋅ 2 = − 8 . And in the variable terms x 8 , and x 9 , since 8 is the smallest exponent to which x is raised, so the GCF of the common variables would be x 8

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ISBN: 9780135257500

Author: Martin-Gay

Publisher: PEARSON

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Chapter 13.1, Problem 85ES

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Factor the polynomial, −40x8y6−16x9y5 .

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Chapter 13.1, Problem 84ES

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Factor the polynomial, − 40 x 8 y 6 − 16 x 9 y 5 .

Solution Summary: The author explains how to factor out the GCF from the given polynomial by rewriting each term as a product of prime factors and identifying the largest factor in all terms.

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Factor the polynomial, −40x8y6−16x9y5 .

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