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

Published by Prentice Hall

# Chapter 8 - Polynomials and Factoring - 8-8 Factoring by Grouping - Got It? - Page 531: 3

#### Answer

The possible dimensions of the prism are $2x,\ 5x+2$ and $6x+1$.

#### Work Step by Step

$60x^{3}+34x^{2}+4x=$ ...factor out the GCF. $=2x(30x^{2}+17x+2)$ ...find factors of $ac$ that have a sum of $b$. ($ac=60,\ b=17$) $\left[\begin{array}{lll} \text{Factors of 60 } & \text{Sum of factors} & \\ 1\text{ and }61 & 62 & \\ 2\text{ and }30 & 32 & \\ 3\text{ and }20 & 23 & \\ 4\text{ and }15 & 19 & \\ 5\text{ and }12 & 17 & \text{ is what we need} \end{array}\right]$ ...use the factors you found to rewrite $bx$. $=2x(30x^{2}+5x+12x+2)$ ...factor by grouping. $=2x[5x(6x+1)+2(6x+1)]$ ...use the Distributive Property. $=2x(5x+2)(6x+1)$ The possible dimensions of the prism are $2x,\ 5x+2$ and $6x+1$.

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