设f（x）以（x-1）除之的余式为8,以x^2+x

设f（x）以（x-1）除之的余式为8,以x^2+x+1除之的余式为7x+16,求f（x）以x^3-1除之的余式为____

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8+a(x-1)+b(x-1)^2=7x+16+c(x^2+x+1),展开比较系数得a=-8,b=-5,c=-5.
故余式为7x+16-5(x^2+x+1)=-5x^2+2x+11