r^4-6r^3+12r^2-8r=o 怎么算出r(r-2)^3=o,
问题描述：
r^4-6r^3+12r^2-8r=o 怎么算出r(r-2)^3=o,
答
r^4-6r^3+12r^2-8r=o
r(r^3-6r^2+12r-8)=0
r[(r^3-2r^2)-(4r^2-8r)+(4r-8)]=0
r[r^2(r-2)-4r(r-2)+4(r-2)]=0
r(r-2)(r^2-4r+4)=0
r(r-2)(r-2)^2=0
r(r-2)^3=0