k(x)=x^5-5x^4+7x^3-2x^2+4x-8有无重因式,如果有请求出重数

有的,是x-2
k(x)=x^5-5x^4+7x^3-2x^2+4x-8
=(x^5-5x^4+6x^3)+(x^3-2x^2)+(4x-8)
=x^3(x-2)(x-3)+x^2(x-2)+4(x-2)
=(x-2)(x^4-3x^3+x^2+4)
=(x-2)(x-2)(x^3-x^2-x-2)
=(x-2)(x-2)[(x^3-1)-(x^2+x+1)]
=(x-2)(x-2)(x-1-1)(x^2+x+1)
=(x^2+x+1)(x-2)^3