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 - Page 275: 73

Answer

$f(x) = (x^4 + 2x^3 - 3x^2 - 4x + 4)$

Work Step by Step

The zeros of this graph are at (-2, 0) and (1,0). At (-2,0) and (1,0) , the graph "bounces" at that point, so that root is a zero with even multiplicity, so it will be to the power of two Thus the polynomial will be $(x+2)^2(x-1)^2$ $f(x) = (x^2 + 4x + 4)(x^2 - 2x +1)$ $f(x) = (x^4 + 2x^3 - 3x^2 - 4x + 4)$
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