2009/032) factor f(x) = x^3-3x^2+4

by taking factors of 4 that is 1,-1.2,-2,4,-4 we see that

f(-1) = 0

so (x+1) is a factor

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