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 443: 15



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. $\quad ac=+15$ 2. $\quad$sum = $-16 \quad$... factors: $-15$ and $-1$ 3. $\quad 5y^{2}-16y+3=(5y^{2}-15y)+(-y+3)$ 4. $\quad$... $=5y(y-3)+(-1)(y-3) =(y-3)(5y-1)$ Check by FOIL$\qquad (y-3)(5y-1)$ = $F:\quad 5y^{2}$ $O:\quad -y$ $I:\quad -15y$ $L:\quad +3$ $(y-3)(5y-1)$ = $5y^{2}-116y+3$
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