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: 8

Answer

$(x-5)(x-8)$

Work Step by Step

The given expression, $ x^2-13x+40 ,$ has $c= 40 $ and $b= -13 .$ The possible factors of $c$ are $ \{ 1,40 \} ,\{ 2,20 \} ,\{ 4,10 \} ,\{ 5,8 \} ,\{ -1,-40 \} ,\{ -2,-20 \} ,\{ -4,-10 \} ,\{ -5,-8 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ -5,-8 \}.$ Hence, the factored form is \begin{array}{l}\require{cancel} (x-5)(x-8) .\end{array}
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