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: 38



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 --- $8x^{2}-22x+5 =...$ Always start by searching for a GCF ... (there are none other than 1). 1. $\quad ac=+40$ 2. $\quad$sum = $-22 \quad$... factors: $-20$ and $-2$ 3. $\quad$ $8x^{2}-22x+5 = (8x^{2}-2x)+( -20x-5)$ 4. $\quad$... $=2x(4x-1) +(-5)(4x-1) = (4x-1)(2x-5)$ Check by FOIL $F:\quad 8x^{2}$ $O:\quad -20x$ $I:\quad -2x$ $L:\quad +5$ $(4x-1)(2x-5)$ = $8x^{2}-22x+5$
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