First, we can factor this to make it easier to solve:
3(x^3 + 13x^2 + 13x + 9)
Now, we can use the rational root theorem like so:
List factors of 9:
1, 3, 9.
List factors of 1:
1
Because of this, we know our possible rational roots are:
+/-1, +/-3, +/-9
If none of these zeros fit using the remainder theorem, then we know our roots will be irrational.
