The Rational Roots Theorem

If the polynomial equation \(a_nx^n + a_n-1x^{n-1} + \dotsb + a_1x + a_0 = 0\) has any rational roots (either whole numbers or fractions) they must be of the form \(\frac{p}{q}\) where \(p\) is a divisor of the constant term \(a_0\) and \(q\) is a divisor of the leading coefficient \(a_n.\)