ANSWER
The correct answer is D.
EXPLANATION
The given function is
[tex]f(x) = 3 {x}^{4} + {x}^{3} - 13 {x}^{2} - 2x + 9[/tex]
According to the rational roots theorem, the possible rational roots of f(x) are all factors of 9 expressed over all the factors of 3,
[tex]\pm \frac{1}{3},\pm \frac{3}{3},\pm \frac{9}{3},\pm9[/tex]
[tex]\pm \frac{1}{3},\pm 1,\pm 3,\pm9[/tex]
The correct answer is D.
