Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.5 - Zeros of Polynomial Functions - Exercise Set - Page 379: 65

Answer

Possible rational zeros can be obtained by using the rational root theorem.

Work Step by Step

Consider the general polynomial $f\left( x \right)={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+...+{{a}_{n}}{{x}^{n}}$ of degree $n$. Follow the following steps to obtain the possible rational zeros: 1. Write all the factors of the constant term ${{a}_{0}}$ and assume they are ${{p}_{i}}$. 2. Write all the factors of the coefficient of term of highest degree ${{a}_{n}}$ and assume they are ${{q}_{i}}$. 3. Write all the possible values of ${{r}_{i}}=\frac{{{p}_{i}}}{{{q}_{i}}}\,\,\text{ and }\,\,-\frac{{{p}_{i}}}{{{q}_{i}}}$. 4. Find all those possible ${{r}_{i}}$ such that $f\left( x={{r}_{i}} \right)=0$ and then $\left( x-{{r}_{i}} \right)$ where ${{r}_{i}}$ gives $f\left( {{r}_{i}} \right)=0$ will be the factors of the polynomial $f\left( x \right)$.
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