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: 62

Answer

$3w^2(w+3)(w+15)$

Work Step by Step

Factoring the $GCF= 3w^2 ,$ the given expression, $ 3w^4+54w^3+135w^2 ,$ is equivalent to \begin{array}{l}\require{cancel} 3w^2(w^2+18w+45) .\end{array} The trinomial expression above has $c= 45 $ and $b= 18 .$ The possible factors of $c$ are $ \{ 1,45 \} ,\{ 3,15 \} ,\{ 5,9 \} ,\{ -1,-45 \} ,\{ -3,-15 \} ,\{ -5,-9 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ 3,15 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} 3w^2(w+3)(w+15) .\end{array}
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