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: 38


The solution set is $\left\{-6, 3\right\}$.

Work Step by Step

Factor the trinomial by looking for the factors of $-18$ whose sum is equal to the coefficient of the middle term ($3$). These factors are $-3$ and $6$. This means that the factored form of the trinomial is $(n-3)(n+6)$. Thus, $n^2+3n-18=0 \\(n-3)(n+6)=0$ Equate each factor to 0; then, solve each equation to obtain: $n-3=0 \text{ or } n+6=0 \\n=3 \text{ or } n=-6$ The solution set is $\left\{-6, 3\right\}$.
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