rational root theoremRationalRootTheorem2001-10-15 22:12:092006-12-02 12:25:45Theorempolynomial\usepackage{amssymb}
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Consider the polynomial
$$p(x)=a_nx^n + a_{n-1}x^{n-1}+\cdots+a_1x+a_0$$
where all the coefficients $a_i$ are integers.
If $p(x)$ has a rational root $u/v$ where $\gcd(u,v)=1$, then
$u| a_0$ and $v| a_n$.
This theorem is related to the result about monic polynomials whose coefficients belong to a unique factorization domain. Such theorem then states that any root in the fraction field is also in the base domain.