Factoring strategies

One useful idea is to factor $p(x)$ over a finite field ${\mathbb{F}}_p$, where $p$ is a very large prime, and all the representatives of the finite field are choosen to lie between $-p/2$ and $p/2$. The prime $p$ must be choosen so large that the coefficients of $p(x)$ and all its factors are in between $-p/2$ and $p/2$. Some techniques for factoring over a finite field are described in the next section.