f = 2x^3-24x^2+70x-48
Need to find all those values of x that make f = 0. i.e.
2x^3-24x^2+70x-48 = 0
x^3-12x^2+35x-24 = 0
By observatiom x = 1 is a solution of the above equation, so take out (x - 1) as a factor.
(x - 1)(x^2 - 11x + 24) = 0 (now factorise the quadratic)
(x - 1)(x - 3)(x - 8) = 0
The zeros of the polynomial are: x = 1, x = 3, x = 8, which are all rational