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: 43

Answer

The solution set is $\left\{2, 14\right\}$.

Work Step by Step

Factor the trinomial by looking for the factors of $28$ whose sum is equal to the coefficient of the middle term ($-16$). These factors are $-14$ and $-2$. This means that the factored form of the trinomial is $(x-14)(x-2)$. Thus, $x^2-16x+28=0 \\(x-14)(x-2)=0$ Equate each factor to 0; then, solve each equation to obtain: $x-14=0 \text{ or } x-2=0 \\x=14 \text{ or } x=2$ The solution set is $\left\{2, 14\right\}$.
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