Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.3 - Factoring Trinomials of the Form x^2+bx+x - Problem Set 6.3: 11

Answer

$(n+4)(n-10)$

Work Step by Step

The following pairs of numbers give a product of $ -40 :$ \begin{array}{l}\require{cancel} \{ 1,-40 \} \text{ } \{ -1,40 \} \text{ } \{ 2,-20 \} \text{ } \{ -2,20 \} \text{ } \{ 4,-10 \} \text{ } \{ -4,10 \} \text{ } \{ -5,8 \} \text{ } \{ 5,-8 \} .\end{array} Of these pairs, the one which gives a sum of $ -6 $ is the pair $\{ 4,-10 \}.$ Hence, the factored form of the given expression, $ n^2-6n-40 $ is \begin{array}{l}\require{cancel} (n+4)(n-10) .\end{array}
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