What are the possible rational zeros of f(x) = 3x4 + x3 − 13x2 − 2x + 9?

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