All the rational zeros of the polynomial: f(x)=2x^3-24x^2+70x-48

Question

Math problem, need help, do not understand how to find the zeros.

Answer 1

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