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oai:uvadoc.uva.es:10324/782082026-04-21T11:39:05Zcom_10324_1145com_10324_931com_10324_894col_10324_1254

General remainder theorem and factor theorem for polynomials over non-commutative coefficient rings Cuida Gómez, María Astrid Laudano, Francesco Martínez Moro, Edgar Producción Científica We propose some generalizations of the classical Division Algorithm for polynomials over coefficient rings (possibly non-commutative). These results provide a generalization of the Remainder Theorem that allows calculating the remainder without using the long division method, even if the divisor has degree greater than one. As a consequence we obtain an extension of the classical Factor Theorem that provides a general divisibility criterion for polynomials. Finally, we will refer to some applications of these results for evaluating and dividing on skew polynomial rings. The arguments can be used in basic algebra courses and are suitable for building classroom/homework activities. 2025-09-30T07:25:51Z 2025-09-30T07:25:51Z 2020 9999-12-31 info:eu-repo/semantics/article International Journal of Mathematical Education in Science and Technology, 2020, v. 51, n. 5, p. 775-785 0020-739X https://uvadoc.uva.es/handle/10324/78208 10.1080/0020739X.2019.1676926 775 5 785 International Journal of Mathematical Education in Science and Technology 51 1464-5211 eng https://www.tandfonline.com/doi/full/10.1080/0020739X.2019.1676926 info:eu-repo/semantics/restrictedAccess © Taylor & Francis Taylor & Francis SI