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 - Practice and Problem-Solving Exercises - Page 521: 33

Answer

Two different values are $-34$ and $41$. $2(r+1)(4r-21)$ and $ (8r-7)(r+6)$.

Work Step by Step

The given expression is $8r^2+\_r-42$ The standard form of the trinomial is $ax^2+bx+c$ Where, $a=8,c=-42$ and $b=?$. Multiply $a$ and $c$. $ac=8\times (-42)=-336$ Two possible factors are $8\times (-42)$ and $48\times (-7)$. So the values of $b$ are $8-42=-34$ and $48-7=41$. The first trinomial is $\Rightarrow 8r^2-34r-42$ Factor. $\Rightarrow 2(r+1)(4r-21)$. The second trinomial is $\Rightarrow 8r^2+41r-42$ Factor. $\Rightarrow (8r-7)(r+6)$.
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