College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.4 - Factoring Polynomials - R.4 Exercises - Page 40: 114

Answer

$c=25$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the concepts of the square of a binomial to find the missing term. $\bf{\text{Solution Details:}}$ Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ then the last term, $b^2,$ is equal to \begin{array}{l}\require{cancel} \left(\dfrac{2ab}{2a} \right)^2 .\end{array} Hence, in the given perfect square trinomial, $ 49x^2+70x+c ,$ where $a=7$ and $2ab=70$, the last term, $c,$ is equal to \begin{array}{l}\require{cancel} \left(\dfrac{70}{2(7)} \right)^2 \\\\= \left(\dfrac{70}{14} \right)^2 \\\\= \left(5\right)^2 \\\\= 25 .\end{array} Hence, $ c=25 .$
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