Using the rational root theorem, we first look at the factors of a_n and a_0:
[tex]\begin{gathered} a_0=9\text{ } \\ \text{Factors: 1,3,9}_{} \\ a_n=2 \\ \text{Factors: 1,2} \end{gathered}[/tex]
Now, finding the possible roots by matching the factors of a_0 with the factors of a_n we get:
[tex]r=\frac{\text{factors of a\_0}}{\text{factors of a\_n}}=\frac{1,3,9}{1,2}=\mleft\lbrace1,3,9,\frac{1}{2},\frac{3}{2},\frac{9}{2}\mright\rbrace[/tex]
As we can see, a possible root of the polynomial solution is 3
