Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Review - Exercises - Page 321: 40

Answer

True; see explanation below

Work Step by Step

The problem asks to prove that a factor is a zero of the polynomial Given $P(x) = x^5 + 4x^4 - 7x^3 - 23x^2 + 23x + 12$ and x+4 Thus the factor is x= -4 Substitute x = -4 into P(x) $P(-4) = (-4)^5 + 4(-4)^4 - 7 (-4)^3 - 23(-4)^2 + 23 (-4) + 12$ $P(-4) = -1024 + 1024 + 448 - 368 - 92 + 12= 0$ Thus x+4 is a zero of the polynomial
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