Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 4 - Quadratic Functions - 4.5 Solving Equations by Factoring - 4.5 Exercises: 19

Answer

$\color{blue}{\left\{-9, -3\right\}}$

Work Step by Step

RECALL: A trinomial of the form $x^2+bx+c$ can be factored if there are integers $d$ and $e$ such that $c=de$ and $b=d+e$. The trinomial's factored form will be: $x^2+bx+c=(x+d)(x+e)$ The trinomial in the given equation has $b=12$ and $c=27$. Note that $27=9(3)$ and $12= 9+3$. This means that $d=9$ and $e=3$ Thus, the factored form of the trinomial is: $(h+9)(h+3)$ The given equation maybe written as: $(h+9)(h+3)=0$ Use the Zero-Factor Property by equating each factor to zero. Then, solve each equation to obtain: \begin{array}{ccc} &h+9 = 0 &\text{ or } &h+3=0 \\&h=-9 &\text{ or } &h=-3 \end{array} Thus, the solution set is $\color{blue}{\left\{-9, -3\right\}}$.
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