$f(x)=3x^2+2$,

$g(x)=x^4+5x^2+2x+2$, in $\mathbb{Z}\_7$.

Find the greatest common divisor $d(x)$ of $g(x)$ and $f(x)$ in $\mathbb{Z}\_7$?

I try to solve, make long division, and find the answer $5x^2+3$ but this answer is wrong.

thank you in advance.