Determine in F 5 [ X ] {\displaystyle {}{\mathbb {F} }_{5}[X]} , using the Euclidean algorithm, the greatest common divisor of the polynomials P = X 4 + 3 X 3 + X 2 + 4 X + 2 {\displaystyle {}P=X^{4}+3X^{3}+X^{2}+4X+2} and Q = 2 X 3 + 4 X 2 + X + 3 {\displaystyle {}Q=2X^{3}+4X^{2}+X+3} .
![{\displaystyle {}{\mathbb {F} }_{5}[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/331da43c9199a772b8d62e29d2918754f18351de)
