ABSTRACT
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 criterion for polynomials. The arguments can be used in basic algebra courses and are suitable for building classroom/homework activities for college and high school students.
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Disclosure statement
No potential conflict of interest was reported by the author.
ORCID
F. Laudano http://orcid.org/0000-0003-4489-095X