Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 3 - Section 3.3 - Dividng Polynomials - 3.3 Exercises: 65

Answer

$P(x)=x^4-8x^3+14x^2+8x-15$

Work Step by Step

RECALL: If $c$ is a zero of a polynomial, then $x-c$ is a factor of the polynomial. Since -1, 1, 3, and 5 are zeros of the polynomial, then $(x+2), (x-1), (x-3), \text{ and } (x-5)$ are factors of the polynomial. Thus, one polynomial of degree 4 with the given zeros is: $\\P(x) =(x+1)(x-1)(x-3)(x-5) \\P(x)=x^4-8x^3+14x^2+8x-15$
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