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: 39



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 --- $9y^{2}-9y+2 =...$ Always start by searching for a GCF ... (there are none other than 1). 1. $\quad ac=+18$ 2. $\quad$sum = $-9\quad$... factors: $-6$ and $-3$ 3. $\quad$ $9y^{2}-9y+2 = ( 9y^{2}-6y)+(-3y+2)$ 4. $\quad$... $= 3y(3y-2)+(-1)(3y-2) = (3y-2)(3y-1)$ Check by FOIL $F:\quad 9y^{2}$ $O:\quad -3y$ $I:\quad -6y$ $L:\quad +2$ $(3y-2)(3y-1)$ = $9y^{2}-9y+2$
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