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

a = 1.

Step-by-step 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.