若不论x取任何值,多项式x³-2x²-4x-1与(x+1)(x²+mx+n)都相等,求m,n
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![若不论x取任何值,多项式x³-2x²-4x-1与(x+1)(x²+mx+n)都相等,求m,n](/uploads/image/z/2096143-7-3.jpg?t=%E8%8B%A5%E4%B8%8D%E8%AE%BAx%E5%8F%96%E4%BB%BB%E4%BD%95%E5%80%BC%2C%E5%A4%9A%E9%A1%B9%E5%BC%8Fx%26%23179%3B-2x%26%23178%3B-4x-1%E4%B8%8E%EF%BC%88x%2B1%EF%BC%89%EF%BC%88x%26%23178%3B%2Bmx%2Bn%EF%BC%89%E9%83%BD%E7%9B%B8%E7%AD%89%2C%E6%B1%82m%2Cn)
若不论x取任何值,多项式x³-2x²-4x-1与(x+1)(x²+mx+n)都相等,求m,n
若不论x取任何值,多项式x³-2x²-4x-1与(x+1)(x²+mx+n)都相等,求m,n
若不论x取任何值,多项式x³-2x²-4x-1与(x+1)(x²+mx+n)都相等,求m,n
答:
多项式x³-2x²-4x-1=(x+1)(x²+mx+n)对任意x都成立.
令x=0,则:n=-1
令x=1,则:2*(1+m+n)=1-2-4-1=-6
所以:m+n=-4
所以:m=-3
所以:m=-3,n=-1