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: 34

Answer

The solution set is $\left\{1, 8\right\}$.

Work Step by Step

Factor the trinomial by looking for the factors of 8 whose sum is equal to the coefficient of the middle term (-9). These factors are $-8$ and $-1$. This means that the factored form of the trinomial is $(x-8)(x-1)$. Thus, $x^2-9x+8=0 \\(x-8)(x-1)=0$ Equate each factor to 0 then solve each equation to obtain: $x-8=0 \text{ or } x-1=0 \\x=8 \text{ or } x=1$ The solution set is $\left\{1, 8\right\}$.
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