Polynomials

Let f(x) = x³ + a·x² + b·x + 18811938 where a and b are integers. If a, b can be selected in such a way that f(x) = 0 has only integer roots, what is the sum of f(-1) for all the possibilities (i.e. all the distinct polynomials that meet the conditions). sum of f_a,b(-1) for a and b that makes f_a,b(x) = 0