Question

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

Answer 1

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

Explanation: