Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 5 - Section 5.4 - Factoring Trinomials - Exercise Set - Page 363: 126

Answer

False

Work Step by Step

We determine the Greatest Common Factor (GCF) and factor it out: $$6y^6-19y^5+10y^4=y^4(6y^2-19y+10).$$ We notice that we can continue factorization of the remaining trinomial: $$y^4(6y^2-19y+10)=y^4(3y-2)(2y-5).$$ Therefore the given statement is FALSE. We change it in order to make it true: Once a GCF is factored from a polynomial, the remaining polynomial factor is SOMETIMES prime.
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