Question

Find the value of a of (x-1) is a factor of the polynomial a^2x^3-4ax+4a-1

Answer 1

a = 1.

Explanation:

By the Factor theorem if (x - 1) is a factor of the polynomial f(x) then f(1) = 0.

So we have:

a^2(1)^3-4a(1)+4a-1 = 0

a^2 - 4a + 4a - 1 = 0

a^2 = 1

a = +/- 1.

Substituting -1 for a

(-1)^21^3-4(-1)1+4*1-1 = 1 + 4 + 4 - 1 = 8 so its can't be -1.

Substituting 1 for a:

(1)^21^3 - 4 + 4 -1 = 0.