Elementary Algebra

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

Chapter 6 - Factoring, Solving Equations, and Problem Solving - Chapter 6 Review Problem Set: 18

Answer

$(3t+1)(7t-4)$

Work Step by Step

In accordance with the rules of factoring trinomials, we need to find two integers whose product is $-84$ and whose sum is $-5$. A little searching determines that these numbers are $7$ and $-12$. Therefore, we can express the middle term $-5t$ as $(7t-12t)$ and proceed to factoring by grouping: $21t^{2}-5t-4$ =$21t^{2}+7t-12t-4$ =$7t(3t+1)-4(3t+1)$ =$(3t+1)(7t-4)$
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