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 - Mid-Chapter Review - Mixed Review: 10

Answer

$(b-7)^2$

Work Step by Step

Using the factoring of trinomials in the form $x^2+bx+c,$ the $\text{ expression }$ \begin{array}{l}\require{cancel} b^2-14b+49 \end{array} has $c= 49 $ and $b= -14 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ -7,-7 \right\}.$ Using these two numbers, the $\text{ expression }$ above is equivalent to \begin{array}{l}\require{cancel} (b-7)(b-7) \\\\= (b-7)^2 .\end{array}
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