Resumen de A generalization of the remainder theorem and factor theorem

F. Laudano

• We propose a generalization of the classical Remainder Theorem for polynomials over commutative coefficient rings that allows calculating the remainder without using the long division method. As a consequence we obtain an extension of the classical Factor Theorem that provides a general divisibility criterionfor polynomials. The arguments can be used in basic algebra courses and are suitable for building classroom/homework activities for college and high school students.