本帖最后由 青青子衿 于 2019-5-20 16:57 编辑
多项式\(\,f(x)=-1+x^5+x^{20}+x^{2019}\,\)除以多项式\(\,g(x)=x^4+x^3+x+1\,\)所得余式为\(\,r(x)\,\),求\(\,r(0)\,\)=?- PolynomialRemainder[-1 + x^5 + x^20 + x^2019, x^4 + x^3 + x + 1, x]
复制代码 ...
...- f[x_]:=-1+x^5+x^20+x^2019
- Df[x_]=D[f[x],x]
- r[x_]:=Subscript[a,0]+Subscript[a,1]x+Subscript[a,2]x^2+Subscript[a,3]x^3
- Dr[x_]=D[r[x],x]
- f[-1]
- Df[-1]
- f[E^((I/3)*Pi)]//FullSimplify
- f[E^(-(I/3)*Pi)]//FullSimplify
- r[-1]
- Dr[-1]
- ...
- Solve[Subscript[a,0]-Subscript[a,1]+Subscript[a,2]-Subscript[a,3]==-2&&
- Subscript[a,1]-2 Subscript[a,2]+3 Subscript[a,3]==2004&&
- Subscript[a,0]+E^((I/3)*Pi) Subscript[a,1]-E^(-(I/3)*Pi) Subscript[a,2]-Subscript[a,3]==-2&&
- Subscript[a,0]+E^(-(I/3)*Pi) Subscript[a,1]-E^((I/3)*Pi) Subscript[a,2]-Subscript[a,3]==-2,
- Subscript[a,#]&/@{0,1,2,3}]
复制代码 https://www.quora.com/unanswered/What-will-be-the-remainder-if-1-x-5-x-20-x-2019-is-divided-by-x-4-x-3-x-1 |