若不论x取何值时,多项式x3-2x2-4x-1与(x+1)(x2+mx+n)都相等.求m,n的值.

问题描述:

若不论x取何值时,多项式x3-2x2-4x-1与(x+1)(x2+mx+n)都相等.求m,n的值.

∵多项式x3-2x2-4x-1与(x+1)(x2+mx+n)都相等,
∴x3-2x2-4x-1=(x+1)(x2+mx+n)=x3+(m+1)x2+(n+m)x+n,
∴m+1=-2,n=-1,m+n=-4,
∴m=-3,n=-1.