Rational roots theorem states that any rational root will be a factor of the constant over a factor of the leading coefficient.
The given equation is: f(x) = 3x^4 + x^3 - 13x^2 - 2x + 9. In this case, it is a factor of 9 over a factor of 3.
Factors of 9: ±1, ±3, ±9
Factors of 3: ±1, ±3
So possible rational roots are: ±1, ±3, ±9, ±1/3