College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.5: 132

Answer

Makes sense.

Work Step by Step

$4x^{2}-100 = (2x+10)(2x-10)$ The first step in factoring the polynomial $4x^{2}-100$ is determining the square roots of each term because it is a binomial. The square of 4x^{2} is 2x, allowing the start of the equation look like this: $(2x ±? )(2x± ? )$. Next, we take a look at the term $-100$. The square root of 100 is 10, allowing the equation to look like this: $(2x±10)(2x±10)$ There is no middle term, meaning sum the squares of 100, must equal zero. Therefore the equation would look like this: $(2x+10)(2x-10)$, making the original statement correct.
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