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: 59

Answer

$x^2(x+2)(x-5)$

Work Step by Step

Factoring the $GCF= x^2 ,$ the given expression, $ x^4-3x^3-10x^2 ,$ is equivalent to \begin{array}{l}\require{cancel} x^2(x^2-3x-10) .\end{array} The trinomial expression above has $c= -10 $ and $b= -3 .$ The possible factors of $c$ are $ \{ 1,-10 \} ,\{ 2,-5 \} \{ -1,10 \} ,\{ -2,5 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ 2,-5 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} x^2(x+2)(x-5) .\end{array}
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