I just learned the Euclidean division, I know the definition, but when doing the exercise, I have no idea what should I begin with.
Here is a question:
Let $f :=X^5+3X^4−2X^3−10X^2−2X+4 ∈ Q[X]$ and $g:=X^4+4X^3+6X^2+5X+2 ∈ Q[X]$ . Using the Euclidean algorithm, compute the greatest common divisor $(\gcd)\,d $ of $ f $ and $ g $ and write down the correspondent $ R[X]$-linear combination: $d(X) = a(X)f(X) + b(X)g(X)$.
Thank you very much in advance.