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: 31

Answer

The solution set is $\left\{-7, -3\right\}$.

Work Step by Step

Factor the trinomial by looking for the factors of 21 whose sum is equal to the coefficient of the middle term (10). These factors are 3 and 7. This means that the factored form of the trinomial is $(x+3)(x+7)$. Thus, $x^2+10x+21=0 \\(x+3)(x+7)=0$ Equate each factor to 0 then solve each equation to obtain: $x+3=0 \text{ or } x+7=0 \\x=-3 \text{ or } x=-7$ The solution set is $\left\{-7, -3\right\}$.
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