Rational Roots of Polynomials with Integer Coefficients

In this note the authors investigate ways to shorten the amount of work involved in using the Rational Roots Theorem to find the rational roots of a polynomial with integral coefficients. The first result is a proof of a fact that we had long suspected, but were never able to find the statement of in any of the college algebra textbooks we had used. The second result is an extension of a theorem due to Ronald Skurnick. This article is appropriate for teachers and students in an introductory college algebra class.