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 $f\left( x \right)$.
