Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.4 Factoring Polynomials - R.4 Exercises: 121

Answer

$b=36$ or $b=-36$

Work Step by Step

RECALL: There are two forms of perfect square trinomials: (1) $m^2+2mn+n^2$, which is the square of $(m+n)^2$; and (2) $m^2-2mn+n^2$, which is the square of $(m-n)^2$ The given trinomial has: $m^2 = 4z^2=(2z)^2$, which means that $m=2z$ $m^2=81=9^2$, which means that $n=9$ Thus, the given trinomial will be a perfect square if (i) $bz=2mn=2(2z)(9) = 36z$, which means that $b=36$; and when (ii) $bz=-2mn=-2(2z)(9) = -36z$, which means that $b=-36$ Therefore, the given polynomial is a perfect square when $b=36$ and when $b=-36$
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