Find the inverse of $[f(z)=3z^2+z+3]$ in $\mathbb{Q}/(z^3-2z-2)$
already prove that polynomial $z^3-2z-2$ is irreducible about $\mathbb{Q}$, now how can I find the inverse of that given polynomial?
someone to please explain to me
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Compare with this duplicate, for example, or this one. – Dietrich Burde Mar 09 '21 at 15:12
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See the dupe (and its links) for how to use the extended Euclidean algorithm. You don't need to first prove it's irreducible. Rather you only need that they are coprime (which the algorithm will determine since it computes their gcd). – Bill Dubuque Mar 09 '21 at 15:18