Does anyone know of a relationship between the constant term of a polynomial and the roots of the polynomial? Specifically, if we know the constant term, is it possible for a root which divides the constant to be a root of the polynomial? Thanks in advance.
The most important part is written slightly lower on the page:
Suppose $P(x)=a_nx^n + \dots + a_0$
is a polynomial with integer coefficients, and $x=\frac pq$ is a rational zero of $P(x)$. Then $p$ divides $a_0$ and $q$ divides $a_n$