(a-1)x³-ax²-(a-3)x+a-2
=[(a-1)x³-(a-1)x²]-(x²-x)-[(a-2)x-(a-2)]
=(a-1)x²(x-1)-x(x-1)-(a-2)(x-1)
=(x-1)[(a-1)x²-x-(a-2)]
=(x-1)(x-1)[(a-1)x+(a-2)]
=(x-1)²[(a-1)x+(a-2)]