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: 44

Answer

The solution set is $\left\{3, 15\right\}$.

Work Step by Step

Factor the trinomial by looking for the factors of $45$ whose sum is equal to the coefficient of the middle term ($-18$). These factors are $-15$ and $-3$. This means that the factored form of the trinomial is $(x-15)(x-3)$. Thus, $x^2-18x+45=0 \\(x-15)(x-3)=0$ Equate each factor to 0; then, solve each equation to obtain: $x-15=0 \text{ or } x-3=0 \\x=15 \text{ or } x=3$ The solution set is $\left\{3, 15\right\}$.
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