Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.4 - Factoring Trinomials of the Form ax^2+bx+c - Problem Set 6.4 - Page 261: 9



Work Step by Step

In accordance with the rules of factoring trinomials, we need to find two integers whose product is $-70$ and whose sum is $-33$. A little searching determines that these numbers are $2$ and $-35$. Therefore, we can express the middle term $-33y$ as $(+2y-35y)$ and proceed to factoring by grouping: $5y^{2}-33y-14$ =$5y^{2}+2y-35y-14$ =$y(5y+2)-7(5y+2)$ =$(5y+2)(y-7)$
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