EXTENDING THE BOX METHOD FOR POLYNOMIAL ARITHMETIC

The box method for performing polynomial multiplication is a popular form of demonstrating the process of multiplying polynomials. This method is graphical, but still lacks the inherent simplicity as well as the organization of like terms. It still requires that combining terms with x’s in the table itself. While this method is very well received and beneficial, we shall extend this further to work solely with numbers and let the table tell us how to combine the values. The purpose of this paper is to demonstrate polynomial arithmetic using tables similar to those constructed for synthetic division. Our focus will be on addition, subtraction and multiplication. Similar to how synthetic division focuses on the coefficients of the polynomials involved, the tables constructed below shall do the same. The advantage to this technique is that it reduces polynomial arithmetic to numerical arithmetic as the table organizes the terms into like terms. How to construct such tables in order to easily perform the arithmetic for students is our primary effort.