if you know how to do synthetic division, it should be easy to show that
x^3-2x^2-9x+18 = (x+3)(x-2)(x-3)
you know that all the roots have to be factors of 18.
use synthetic division to factor x^3-2x^2-9x+18
2 answers
x^3-2x^2-9x+18 = (x+3)(x-2)(x-6)