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: 53



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 --- $2a^{2}+7ab+5b^{2} =...$ Always start by searching for a GCF ... (there are none other than 1). 1. $\quad$"$ac$"$=+10b^{2} $ 2. $\quad$sum = $+7b\quad$... factors: $2b$ and $5b$ 3. $\quad$ $2a^{2}+7ab+5b^{2} = (2a^{2}++2ab)+( 5ab+5b^{2})$ 4. $\quad$... $= 2a(a+b)+5b(a+b) = (2a+5b)(a+b)$ Check by FOIL $F:\quad 2a^{2}$ $O:\quad +2ab$ $I:\quad +5ab$ $L:\quad +5b^{2}$ $(2a+5b)(a+b)$ = $2a^{2}+7ab+5b^{2}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.