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: 57

Answer

$y^2(y+8)(y-10)$

Work Step by Step

Factoring the $GCF= y^2 ,$ the given expression, $ y^4+2y^3-80y^2 ,$ is equivalent to \begin{array}{l}\require{cancel} y^2(y^2-2y-80) .\end{array} The trinomial expression above has $c= -80 $ and $b= -2 .$ 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 of the given expression is \begin{array}{l}\require{cancel} y^2(y+8)(y-10) .\end{array}
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