Verified answer

Long division method.

(x^3-4x^2)/(x-1) = x^2 remainder -3x^2 to carry

(-3x^2+5x)/(x-1) =-3x remainder 2x to carry

(2x-2)/(x-1)=2

Adding these parts back together

Answer = x^2-3x+2

Well, the roots are x = 1 (twice) and x = 2, so it's (x-2)(x-1)(x-1), and thus the result is (x-2)(x-1)

The answer is x^2-3x+2=(x-2)(x-1)