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: 35

Answer

The solution set is $\left\{-2, 5\right\}$.

Work Step by Step

Factor the trinomial by looking for the factors of $-10$ whose sum is equal to the coefficient of the middle term ($-3$). These factors are $-5$ and $2$. This means that the factored form of the trinomial is $(x-5)(x+2)$. Thus, $x^2-3x-10=0 \\(x-5)(x+2)=0$ Equate each factor to 0 then solve each equation to obtain: $x-5=0 \text{ or } x+2=0 \\x=5 \text{ or } x=-2$ The solution set is $\left\{-2, 5\right\}$.
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