MathNet 2015-part-07 — 185 problems (EN–VI) Question 68

Let $P(x) = x^{3} + a x^{2} + b x + 2015$ be a polynomial all of whose roots are integers. Given that $P(x) \geq 0$ for all $x \geq 0$, find the sum of all possible values of $P(-1)$.