Factoring Quadratic x²+bx+c with c<0

Suppose we can write $x^2+bx-2018 = (x+p)(x+q)$ where $p$ and $q$ are (not necessarily positive) integers. Check off all possible values of $b$.

(Recall that the prime factorization of $2018$ is $2018 = 2 \cdot 1009$.)