Euclidean algorithm (polynomial ring)/Gcd/R/X^3+pi X^2+7 and X^2+sqrt7X-sqrt2/Exercise

Determine in ${}\mathbb {R} [X]$, using the Euclidean algorithm, the greatest common divisor of the polynomials ${}P=X^{3}+\pi X^{2}+7$ and ${}Q=X^{2}+{\sqrt {7}}X-{\sqrt {2}}$.

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