find a formula that depends on p that determines the number of reducible monic degree 2 polynomials over Zp. so the polynomials look like x^2+ax+b with a,b in Zp. I examined the case for Z3 and Z5 to try and see what was going on. in Z3 we had 9 monic degree 2 polynomials, 6 of them were reducible and 3 were not. in Z5 we had 25 monic degree 2's 15 were reducible and 10 were not. it appears that (p(p+1))/2 is the formula but just showing two cases is obviously not enough work. Is my guess right and how on earth would I prove it. thanks!