Perform in the polynomial ring Q [ X ] {\displaystyle {}\mathbb {Q} [X]} the division with remainder P T {\displaystyle {}{\frac {P}{T}}} , where P = 5 X 4 − 6 X 3 + 3 5 X 2 − 1 2 X + 5 {\displaystyle {}P=5X^{4}-6X^{3}+{\frac {3}{5}}X^{2}-{\frac {1}{2}}X+5} and T = 1 7 X 2 + 3 7 X − 1 {\displaystyle {}T={\frac {1}{7}}X^{2}+{\frac {3}{7}}X-1} .
![{\displaystyle {}\mathbb {Q} [X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/05854fb7f5090d865105d7297fa178c8eb802fbf)
