m、n为何值时,多项式x^4-5x^3+mx+n能被x^2-2x+1整除?

m、n为何值时,多项式x^4-5x^3+mx+n能被x^2-2x+1整除?
m、n为何值时,多项式x^4-5x^3+mx+n能被x^2-2x+1整除?

m、n为何值时,多项式x^4-5x^3+mx+n能被x^2-2x+1整除?
x^4-5x^3+11x^2+mx+n
=(x^2-2x+1)(x^2+ax+n)
=x^4+(a-2)x^3+(n-2a+1)x^2+(a-2n)x+n
a-2=-5
n-2a+1=11
a-2n=m
a=-3,n=4,m=-11
余式x^2-3x+4