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: 40


The solution set is $\left\{-4, 12\right\}$.

Work Step by Step

Factor the trinomial by looking for the factors of $-48$ whose sum is equal to the coefficient of the middle term ($-8$). These factors are $-12$ and $4$. This means that the factored form of the trinomial is $(n-12)(n+4)$. Thus, $n^2-8n-48=0 \\(n-12)(n+4)=0$ Equate each factor to 0; then, solve each equation to obtain: $n-12=0 \text{ or } n+4=0 \\n=12 \text{ or } n=-4$ The solution set is $\left\{-4, 12\right\}$.
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