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 - Page 359: 33

Answer

Elijah was wrong because he did not write the equation in $x^2+bx+c=0$ form before factoring. The solution set is $\left\{-4, -1\right\}$.

Work Step by Step

Elijah was wrong because he did not write the equation in the form $x^2+bx+c=0$ before factoring. The Zero-Product Property can only be used for equations in the form $ab=0$. The correct work is the one below: \begin{align*} x^2+5x+6-2&=0\\ x^2+5x+4&=0\\ (x+4)(x+1)&=0\\ x+4&=0 &\text{or}& &x+1=0\\ x&=-4 &\text{or}& &x=-1\end{align*}
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