Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - Connecting: The Concepts - Exercises - Page 350: 7



Work Step by Step

The given expression is equivalent to: $t^2−10^2=0$ Factor the binomial using the formula $a^2−b^2=(a−b)(a+b)$ with $a=t$ and $b=10$ to obtain: $(t−10)(t+10)=0$ RECALL: The zero factor theorem states that if $a\cdot b=0$, then either $a=0$ or $b=0$ or both are zero. Equate each factor to zero, then solve for $t$: $t−10=0 \\t−10+10=0+10 \\t=10$ or $t+10=0 \\t+10−10=0−10 \\t=−10$ Thus, the solution set is $\color{blue}{\left\{−10,10\right\}}$.
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