Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 6 - Section 6.2 - Factoring Trinomials Whose Leading Coefficient is 1 - Exercise Set: 42

Answer

$(a-8b)(a-10b)$

Work Step by Step

The given expression, $ a^2-18ab+80b^2 ,$ has $c= 80 $ and $b= -18 .$ The possible factors of $c$ are $ \{ 1,80 \} ,\{ 2,40 \} ,\{ 4,20 \} ,\{ 5,16 \} ,\{ 8,10 \} ,\{ -1,-80 \} ,\{ -2,-40 \} ,\{ -4,-20 \} ,\{ -5,-16 \} ,\{ -8,-10 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ -8,-10 \}.$ Hence, the factored form is \begin{array}{l}\require{cancel} (a-8b)(a-10b) .\end{array}
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