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: 35


$ (2y+9)(5y-1)$

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 --- $10y^{2}+43y-9 =...$ Always start by searching for a GCF ... (there are none other than 1). 1. $\quad ac=-90\qquad $ 2. $\quad$sum = $+43 \quad$... factors: $+45$ and $-2$ 3. $\quad 10y^{2}+43y-9 = (10y^{2}+45y)+(-2y-9)$ 4. $\quad$... $= 5y(2y+9)+(-1)(2y+9)=(2y+9)(5y-1)$ Check by FOIL $F:\quad 10y^{2}$ $O:\quad -2y$ $I:\quad +45y$ $L:\quad -9$ $ (2y+9)(5y-1)$ = $10y^{2}+43y-9$
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