m、n为何值时,多项式x^4-5x^3+mx+n能被x^2-2x+1整除?
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![m、n为何值时,多项式x^4-5x^3+mx+n能被x^2-2x+1整除?](/uploads/image/z/1790969-41-9.jpg?t=m%E3%80%81n%E4%B8%BA%E4%BD%95%E5%80%BC%E6%97%B6%2C%E5%A4%9A%E9%A1%B9%E5%BC%8Fx%5E4-5x%5E3%2Bmx%2Bn%E8%83%BD%E8%A2%ABx%5E2-2x%2B1%E6%95%B4%E9%99%A4%3F)
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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