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: 8


$(x-3)(5x-2) $

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.... none (other than 1). 1. $ac=30$ 2. sum = $-17$ ... factors: $-15$ and $-2$ 3. $5x^{2}-17x+6=(5x^{2}-15x)+(-2x+6)$ 4. ... $=5x(x-3)+(-2)( x-3)$ $=(x-3)(5x-2)$ Check by FOIL$\qquad (x-3)(5x-2) $= $F:\quad 5x^{2}$ $O:\quad -2x$ $I:\quad -15x$ $L:\quad +6$ $(x-3)(5x-2) $= $5x^{2}-17x+6$
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