试将多项式试将多项式f(x)=x^4+x^3+2x^2+1展开成（x-1）的乘幂形式。 非常感谢。求高手

x^4+x^3+2x^2+1
=x^3(x-1)+2x^3+2x^2+1
=x^3(x-1)+2x^2(x-1)+4x^2+1
=x^3(x-1)+2x^2(x-1)+4x(x-1)+4x+1
=x^3(x-1)+2x^2(x-1)+4x(x-1)+4(x-1)+5
=(x^3+2x^2+4x+4)(x-1)+5
=[x^2(x-1)+4x^2+4x+4](x-1)+5
=[x^2(x-1)+4x(x-1)+8x+4](x-1)+5
=[x^2(x-1)+4x(x-1)+8(x-1)+12](x-1)+5
=[(x^2+4x+8)(x-1)+12](x-1)+5
={[(x(x-1)+5x+8](x-1)+12}(x-1)+5
={[x(x-1)+5(x-1)+13](x-1)+12}(x-1)+5
={[(x+5)(x-1)+13](x-1)+12}(x-1)+5
=【{[(x-1)+6](x-1)+13}(x-1)+12]】(x-1)+5
={[(x-1)^2+6(x-1)+13](x-1)+12}(x-1)+5
=[(x-1)^3+6(x-1)^2+13(x-1)+12](x-1)+5
=(x-1)^4+6(x-1)^3+13(x-1)^2+12(x-1)+5

个人感觉不太可能 f(1)不等于0

=(x-1)^4+5(x-1)^3+11(x-1)^2+11(x-1)+5