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: 25


$(2y+3)(7y-3) $

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 --- Always start by searching for a GCF ... (there are none other than 1). 1. $\quad ac=-126\qquad (2\times 63=2\times 7\times 9=2\times 3\times 3\times 7)$ 2. $\quad$sum = $+15 \quad$... factors: $+21$ and $-6$ 3. $\quad 14y^{2}+15y-9=(7y^{2}+21y)+(-6y-9)$ 4. $\quad$... $=7y(2y+3)+(-3)(2y+3) =(2y+3)(7y-3)$ Check by FOIL $F:\quad 14y^{2}$ $O:\quad -6y$ $I:\quad +21y$ $L:\quad -9$ $(2y+3)(7y-3) $ = $14y^{2}+15y-9$
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