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: 52



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 --- $15x^{2}-31xy+10y^{2} =...$ Always start by searching for a GCF ... (there are none other than 1). 1. $\quad ac=+150y^{2} \quad(150=6\times 25)$ 2. $\quad$sum = $-31y\quad$... factors: $-6y$ and $-25y$ 3. $\quad$ $15x^{2}-31xy+10y^{2} = (15x^{2}-25xy)+(-6xy+10y^{2} )$ 4. $\quad$... $= 5x(3x-5y)+(-2y)(3x-5y) = (5x-2y)(3x-5y)$ Check by FOIL $F:\quad 15x^{2}$ $O:\quad -25xy$ $I:\quad -6xy$ $L:\quad +10y^{2}$ $(5x-2y)(3x-5y)$ = $15x^{2}-31xy+10y^{2}$
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