The rational zeros theorem states that the possible rational roots of a polynomial are given by the factors of the constant term divided by the factors of the lead coefficient.
In the given polynomial f(x), the constant term is -9 and the lead coefficient is also -9.
The factors of -9 are:
[tex]\pm1,\pm3,\pm9[/tex]Therefore the possible rational roots are:
[tex]\begin{gathered} possible\text{ }rational\text{ }roots=\frac{\pm1,\pm3,\pm9}{\pm1,\pm3,\pm9}\\ \\ =\pm\frac{1}{9},\pm\frac{1}{3},\pm1,\pm3,\pm9 \end{gathered}[/tex]
