Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 8 - Polynomials and Factoring - 8-6 Factoring ax2+bx+c - Got It? - Page 519: 1


a. $(2x+1)(3x+5)$ b. The factors are both negative.

Work Step by Step

a. Find factors of $ac$ that have a sum of $b$. Since $ac=30$ and $b=13$, find positive factors of $30$ with a sum of $13$. $\left[\begin{array}{lll} \text{Factors of 30 } & \text{Sum of factors} & \\ 1\text{ and }30 & 31 & \\ 2\text{ and }15 & 17 & \\ 3\text{ and }10 & 13 & \text{is what we need} \end{array}\right]$ $6x^{2}+13x+5$ ...use the factors to rewrite $bx$. $=6x^{2}+3x+10x+5$ ...factor out the GCF out of each pair of terms. $=3x(2x+1)+5(2x+1)$ ...use the Distributive Property. $=(2x+1)(3x+5)$ --- b. The factors are both negative. In order to have a positive product both factors must be either positive or negative. In this case, $b$ is negative, so $a $ and $c$ must give a negative sum and a positive product.
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