Use the rational zero theorem to create a list of all possible rational zeros of the function f (x) = 14x7-4x2+2

Factor this polynomial:

F (x) = x^3-x^2-4x+4

Try to find the rational roots. If p/q is a root (p and q having no factors in common), then p must divide 4 and q must divide 1 (the coefficient of x^3).

The rational roots can thuis be + / 1, + / 2 and + / 4. If you insert these values you find that the roots are at

x = 1, x = 2 and x = - 2. This means that

x^3-x^2-4x+4 = A (x - 1) (x - 2) (x + 2)

A = 1, as you can see from equation the coefficient of x^3 on both sides.

Typo:

The rational roots can be

+/-1, + / -2 and + / -4