The Generalized Remainder and Quotient Theorems

TL;DR

This paper extends the generalized remainder and quotient theorems for polynomials to cases where the divisor is not fully factorized into linear factors, broadening their applicability.

Contribution

It provides new formulas for the generalized remainder and quotient theorems applicable to polynomials with divisors that are not completely factorized into linear factors.

Findings

New formulas for generalized remainder theorem

New formulas for generalized quotient theorem

Broader applicability to polynomial division

Abstract

The author in [7] was proved the generalized remainder and quotient theorems of polynomial in one indeterminate where the divisor is complete factorization to linear factors. In this paper we give the formula for the generalized remainder theorem and the generalized quotient theorem of polynomials when the divisor is not factorization to linear factors.