f(x)=x^3-2x^2-5x+6
Note, that if we can add the coefficients of a polynomial and we get "0," then 1 is a root (or, zero)..therefore....
1 - 2 - 5 + 6
-1 + 1 = 0 So 1 is a root
So, using a little synthetic division, we have
1 1 -2 -5 6
1 -1 -6
1 -1 -6 0
So, the polynomial that remains is x2 -x -6 which can be factored as....
(x-3) (x + 2)
And the factorization is (x-1) (x-3) (x +2) and the rational zeroes obtained by setting each factor to 0 are 1, 3 and -2
And that's it.....