Führe in ( Q [ 3 ] ) [ X ] {\displaystyle {}(\mathbb {Q} [{\sqrt {3}}])[X]} die Division mit Rest „ P {\displaystyle {}P} durch T {\displaystyle {}T} “ für die beiden Polynome P = 3 X 3 − ( 2 + 3 ) X 2 + 5 3 X + 1 + 2 3 {\displaystyle {}P=3X^{3}-(2+{\sqrt {3}})X^{2}+5{\sqrt {3}}X+1+2{\sqrt {3}}} und T = 3 X 2 − X + 2 + 7 3 {\displaystyle {}T={\sqrt {3}}X^{2}-X+2+7{\sqrt {3}}} durch.
![{\displaystyle {}(\mathbb {Q} [{\sqrt {3}}])[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/178055c1eb9eaeceab7d75f1a6c68060ecbdd0f2)
