Guess Solutions of Polynomials

For a given polynomial of $n$th degree $$P_n(x)=\sum_{i=0}^n a_ix^i = a_nx^n+a_{n-1}x^{n-1}+…+a_1x+a_0$$ you can guess rational solutions $x$ for the corresponding problem $P_n(x)=0$ by applying the following two rules: $$x=\frac{p}{q}\text{, with } p \in \mathbb{Z} \land q \in \mathbb{N}\land p\mid a_0 \land […]