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: 58

Answer

$y^2(y-5)(y-7)$

Work Step by Step

Factoring the $GCF= y^2 ,$ the given expression, $ y^4-12y^3+35y^2 ,$ is equivalent to \begin{array}{l}\require{cancel} y^2(y^2-12y+35) .\end{array} The trinomial expression above has $c= 35 $ and $b= -12 .$ The possible factors of $c$ are $ \{ 1,35 \} ,\{ 5,7 \} ,\{ -1,-35 \} ,\{ -5,-7 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ -5,-7 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} y^2(y-5)(y-7) .\end{array}
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