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: 41



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 --- $20x^{2}+27x-8 =...$ Always start by searching for a GCF ... (there are none other than 1). 1. $\quad ac=-160 \quad$...$ (160=5\times 32)$ 2. $\quad$sum = $+27\quad$... factors: $+32$ and $-5$ 3. $\quad$ $20x^{2}+27x-8 = (20x^{2}-5x)+(32x-8 )$ 4. $\quad$... $= 5x(4x-1)+8(4x-1) =(4x-1)(5x+8)$ Check by FOIL $F:\quad 20x^{2}$ $O:\quad +32x$ $I:\quad -5x$ $L:\quad -8$ $(4x-1)(5x+8)$ = $20x^{2}+27x-8$
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