Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set: 55

Answer

$(x+z)(x+7z)$

Work Step by Step

The two numbers whose product is $ac= 1(7)=7 $ and whose sum is $b= 8 $ are $\{ 1,7 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ x^2+8xz+7z^2 $, is \begin{array}{l}\require{cancel} x^2+xz+7xz+7z^2 \\\\= (x^2+xz)+(7xz+7z^2) \\\\= x(x+z)+7z(x+z) \\\\= (x+z)(x+7z) .\end{array}
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