## Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 8 - Polynomials and Factoring - 8-8 Factoring by Grouping - Practice and Problem-Solving Exercises - Page 532: 30

#### Answer

The possible dimensions of the trunk are $2x,\ 3x-2$ and $x+7$.

#### Work Step by Step

$6x^{3}+38x^{2}-28x=$ ...factor out the GCF. $=2x(3x^{2}+19x-14)$ ...find factors of $ac$ that have a sum of $b$. ($ac=-42,\ b=19$) $\left[\begin{array}{lll} \text{Factors of 60 } & \text{Sum of factors} & \\ 1\text{ and }-19 & -18 & \\ -1\text{ and }19 & 18 & \\ 2\text{ and }-21 & -19 & \\ -2\text{ and }21 & 19 & \text{ is what we need} \end{array}\right]$ ...use the factors you found to rewrite $bx$. $=2x(3x^{2}+21x-2x-14)$ ...factor by grouping. $=2x[3x(x+7)-2(x+7)]$ ...use the Distributive Property. $=2x(3x-2)(x+7)$ The possible dimensions of the trunk are $2x,\ 3x-2$ and $x+7$.

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