按(x+1)的乘幂展开多项式x^5-2x^2+2x-1

2025-04-07 20:11:37
推荐回答(3个)
回答1:

用泰勒公式,原式=(x+1)'5-5(x+1)'4+10(x+1)'3-12(x+1)'2+11(x+1)-6

回答2:

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

回答3:

(x+1)^5-5(x+1)^4+10(x+1)^3-12(x+1)^2+11(x+1)-6