## Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole

# Chapter 3 - Exponents, Polynomials and Functions - 3.5 Special Factoring Techniques - 3.5 Exercises - Page 279: 40

#### Answer

$3(2w^5+5)(w^5-7)$

#### Work Step by Step

First, pull out the greatest common factor. The remaining terms do not form a perfect square, but we can still factor using another method. To factor when the coefficient of the first term is greater than $1$, determine the two numbers that, when multiplied, equal the coefficient of the first term times the third term, and, when added, equal the coefficient of the middle term. Next, group the four terms into two sets of parentheses and pull out the greatest common factors in each. $6w^{10}-27w^5-105$ $=3(2w^{10}-9w^5-35)$ $=3(2w^{10}-14w^5+5w^5-35)$ $=3[(2w^{10}-14w^5)+(5w^5-35)]$ $=3[2w^5(w^5-7)+5(w^5-7)]$ $=3(2w^5+5)(w^5-7)$

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