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… Click to show full abstract
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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