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: 41

Answer

The solution set is $\left\{-8, 7\right\}$.

Work Step by Step

Factor the trinomial by looking for the factors of $-56$ whose sum is equal to the coefficient of the middle term ($1$). These factors are $-7$ and $8$. This means that the factored form of the trinomial is $(t-7)(t+8)$. Thus, $t^2+t-56=0 \\(t-7)(t+8)=0$ Equate each factor to 0; then, solve each equation to obtain: $t-7=0 \text{ or } t+8=0 \\t=7 \text{ or } t=-8$ The solution set is $\left\{-8, 7\right\}$.
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