The problem statement, all variables and given/known data Let p be a prime. (a) Determine the number of irreducible polynomials over Zp of the form x2 + ax + b. (b) Determine the number of irreducible quadratic polynomials over Zp. The attempt at a solution A nonzero, nonunit polynomial f(x) in Zp[x] is irreducible if it equals the product of two polynomials in Zp[x], one of them being a unit of Zp[x]. But does Zp[x] have any units? I find it hard to imagine that there are polynomials g(x) and h(x) in Zp[x] with g(x)h(x) = 1, unless of course g(x) = h(x) = ±1.