Let p be a prime,
(a) How many monic quadratic (degree 2) polynomials x2 + bx + c in Zp[x] can we factor into linear factors in Zp[x]? (For example, if p = 5, then the polynomial x2 + 2x + 2 in Z5[x] would be one of the quadratic polynomials for which we should account, under these conditions.)
(b) How many quadratic polynomials ax2 + bx + c in Zp[x] can we factor into linear factors in Zp[x]?
(c) How many monic quadratic polynomials x2 + bx + c in Zp[x] are irreducible over ZP?
(d) How many quadratic polynomials ax2 + bx + c in Zp[x] are irreducible over Zp?