Problem:
Let $f(x)$ be a quartic polynomial with integer coefficients and four integer roots. Suppose the constant term of $f(x)$ is $6$.
(a) Is it possible for $x=3$ to be a root of $f(x)$?
(b) Is it possible for $x=3$ to be a double root of $f(x)$?
Prove your answers.
What I know:
For a rational number $\frac{p}{q}$ to be a root of a polynomial $a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0$, $p$ must divide $a_0$ and $q$ must divide $a_n.$
How to I complete this problem?