关于多项式综合除法的推广应用

多项式是现代数学最重要的概念和工具之一，所谓多项式长除法就是多项式与多项式做类似于数与数的除法，其在求多项式因式分解、求多项式切线、求积分、求导、求解微分方程及线性代数中的求逆等问题中有着广泛应用。长除法的计算虽然不需要任何技巧，但其计算过程非常冗长。为了简化多项式长除法的运算过程，使其在实际运用中更容易操作，本文在多项式综合除法的基础上，对多项式长除法进行探讨，并推出一种多项式除法，称为短除法。

The Generalized Application on Synthetic Division of Polynomials

Polynomial is one of the most important concepts and tools of modem mathematics. Long division of polynomials like the division of numbers is very useful in a large area of mathematics such as factorization of polynomials, finding tangent of polynomials, integrations, derivations, and solving differential equations and inverse problem in the liner algebra. Calculation of the long division of polynomials doesn＇t need any special techniques, but the process of the calculation is very tedious and inconvenient. In this paper, in order to simplify the process of the long division and make it easy to use, long division of polynomials is being transformed by using synthetic division of polynomial, obtaining the generalized application of synthetic division of polynomials.