令x=1 则上式=0
故代数式必有因式(x-1)
上式=(x-1)^3-8(x-1)^2+12(x-1)
=(x-1)[(x-1)^2-8(x-1)+12]
=(x-1)(x^2-10x+21)
=(x-1)(x-3)(x-7)