Determine in Q [ X ] {\displaystyle {}\mathbb {Q} [X]} , using the Euclidean algorithm, the greatest common divisor of the polynomials P = X 3 + 2 X 2 + 5 X + 2 {\displaystyle {}P=X^{3}+2X^{2}+5X+2} and Q = X 2 + 4 X − 3 {\displaystyle {}Q=X^{2}+4X-3} .
![{\displaystyle {}\mathbb {Q} [X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/05854fb7f5090d865105d7297fa178c8eb802fbf)
