Elementary Algebra

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

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.3 - Factoring Trinomials of the Form x^2+bx+x - Problem Set 6.3 - Page 255: 14



Work Step by Step

To factor a trinomial in the form $x^2+bx+c$, we must find two numbers whose product is $c$ and whose sum is $b$. We then insert these two numbers into the blanks of the factors $(t+\_)(t+\_)$. In the case of $t^2+20t+96$, we are looking for two numbers whose product is $96$ and whose sum is $20$. The numbers $8$ and $12$ meet these criteria because $$8\times12=96\;\text{and}\;8+12=20$$When we insert these numbers into the blanks, we arrive at the factors $(t+8)(t+12).$
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