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 - Lesson Check - Page 520: 1



Work Step by Step

Find factors of $ac$ that have a sum of $b$. Since $ac=15$ and $b=16$, find factors of $15$ with a sum of $16$. $\left[\begin{array}{lll} \text{Factors of 15 } & \text{Sum of factors} & \\ 1\text{ and }15 & 16 & \text{...what we need} \end{array}\right]$ $3x^{2}+16x+5$ ...use the factors to rewrite $bx$. $=3x^{2}+x+15x+5$ ...factor out the GCF out of each pair of terms. $=x(3x+1)+5(3x+1)$ ...use the Distributive Property. $=(3x+1)(x+5)$
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