Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 5 Polynomials and Polynomial Functions - 5.5 Apply the Remainder and Factor Theorems - 5.5 Exercises - Skill Practice - Page 356: 38a


See below.

Work Step by Step

The Factor Theorem says that if $f(x)$ is a polynomial then it has a factor $x- a$ if and only if $f(a) = 0$. Hence here $x-2$ is a factor of $f(x)$, thus: $f(x)=x^3-5x^2-12x+36=(x-2)(x^2-3x-18)=(x-2)(x+3)(x-6)$
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