 If the coefficients contain a common factor greater than 1 or if the discriminant Δ = "b"2 − 4"ac" is a perfect square, the polynomial factorizes and therefore produces composite numbers as "x" takes the values 0, 1, 2, ... (except possibly for one or two values of "x" where one of the factors equals 1).Moreover, if "a" + "b" and "c" are both even, the polynomial produces only even values, and is therefore composite except possibly for the value 2.Hardy and Littlewood assert that, apart from these situations, "ax"2 + "bx" + "c" takes prime values infinitely often as "x" takes the values 0, 1, 2, ...