Primitive polynomials I am revising for a discrete mathematics exam and as quite stuck on this question.
Show that the polynomial $f = x^2 + 2 x + 3 \in \mathbb{Z}_5[x]$ is primitive. How many monic primitive quadratic polynomials are there in $\mathbb{Z}_5[x]$?
Any help would be greatly appreciated.

Hint: if you actually meant "irreducible polynomial"  then
$$x^2+2x+3\in\Bbb Z_5[x]\implies \Delta=b^2-4ac=4-12=-8=2\pmod 5$$
Is there $\,a\in\Bbb Z_5\;\;s.t.\,\,a^2=2\,$ ?
