An Algorithm For Computing Quotient And Remainder Polynomials

The task of dividing one polynomial by another is encountered in continuous fraction expansion (CFE) and other engineering and systems science computations. This note presents an efficient algorithm for performing the division. A method for constructing synthetic division tableaus (SDT) for polynomials over any coefficient field is formulated and the relative ease in extracting the solution from the tableau is demonstrated. The beauty of the method lies in its simplicity even for manual calculations; and above its efficiency, a minimal memory space is needed for program execution. While other programs and algorithms exist for performing this task, the algorithm introduced in this correspondence promises high efficiency and simplicity in formulation than many of the existing methods. To demonstrate its effectiveness and efficiency, the new method is compared to other existing methods.