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: 54



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