Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.2 - Factoring the Difference of Two Squares - Problem Set 6.2: 57

Answer

The solution set is $\left\{-4, 0, 4\right\}$.

Work Step by Step

Factor out $3x$ to obtain: $3x(x^2-16)=0 \\3x(x^2-4^2)=0 \\3x(x-4)(x+4)=0$ RECALL: A difference of two squares can be factored using the formula: $a^2-b^2=(a-b)(a+b)$ Factor the difference of two squares to obtain: $3x(x-4)(x+4)=0$ Equate each factor to 0, and then solve each equation to obtain: $3x=0 \text{ or } x-4=0 \text{ or } x+4 = 0\\\ x=0 \text{ or } x=4 \text{ or } x=-4$ The solution set is $\left\{-4, 0, 4\right\}$.
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