Remainder and quotient without polynomial long division

Francesco Laudano ^[1]
1. [1] University of Molise
  
  University of Molise
  
  Campobasso, Italia
Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 52, Nº. 7, 2021, págs. 1113-1123
Idioma: inglés
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Resumen
- We propose an algorithm that allows calculating the remainder and the quotient of division between polynomials over commutative coefficient rings, without polynomial long division. We use the previous results to determine the quadratic factors of polynomials over commutative coefficient rings and, in particular, to completely factorize in Z[x] any integral polynomial with degree less than 6. The arguments are suitable for building classroom/homework activities in basic algebra courses.