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: 49


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

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 --- $6x^{2}-5xy-6y^{2} =...$ Always start by searching for a GCF ... (there are none other than 1). 1. $\quad ac=-36y^{2} $ 2. $\quad$sum = $-5y\quad$... factors: $-9y$ and $+4y$ 3. $\quad$ $6x^{2}-5xy-6y^{2} = (6x^{2}-9xy)+(4xy-6y^{2} )$ 4. $\quad$... $= 3x(2x-3y)+(2y)(2x-3y) = (3x+2y)(2x-3y)$ Check by FOIL $F:\quad 6x^{2}$ $O:\quad -9xy$ $I:\quad +4xy$ $L:\quad -6y^{2}$ $ (3x+2y)(2x-3y)$ = $6x^{2}-5xy-6y^{2}$
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