When the integer case,
$ \gcd (a, 0 ) = a$ for $a( \neq 0) \in \mathbb Z$
Plus people generally said $\gcd(0,0)$ can't be defined.
When we expand this consideration by the polynomials ring $F[x]$ for a field, $F$
What about the case $\gcd(f(x), 0)$ ? (Here the $f (\neq 0) \in F[x]$, $0$ is $0$ a polynomial in $F[x]$)
plus Could I regard the case $\gcd(0,0)$ Can't be defined like the integer case?