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: 33

Answer

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

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 (-9). These factors are $-6$ and $-3$. This means that the factored form of the trinomial is $(x-6)(x-3)$. Thus, $x^2-9x-18=0 \\(x-6)(x-3)=0$ Equate each factor to 0 then solve each equation to obtain: $x-6=0 \text{ or } x-3=0 \\x=6 \text{ or } x=3$ The solution set is $\left\{3, 6\right\}$.
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