Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 6 - Section 6.3 - Factoring Trinomials Whose Leading Coefficient is Not 1 - Exercise Set - Page 444: 24


$ (x+8)(3x-2) $

Work Step by Step

Factoring by grouping: 1. Multiply the leading coefficient, a, and the constant, c. 2. Find the factors of ac whose sum is b. 3. Rewrite the middle term, bx, as a sum or difference using the factors from step 2. 4. Factor by grouping --- Always start by searching for a GCF ... (there are none other than 1). 1. $\quad ac=-48$ 2. $\quad$sum = $+22 \quad$... factors: $+24$ and $-2$ 3. $\quad 3x^{2}+22x-16 =(3x^{2}+24x)+( -2x-16)$ 4. $\quad$... $=3x(x+8) +(-2)(x+8) =(x+8)(3x-2)$ Check by FOIL $F:\quad 3x^{2}$ $O:\quad -2x$ $I:\quad +24x$ $L:\quad -16$ $ (x+8)(3x-2) $ = $3x^{2}+22x-16$
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