ABSTRACT
A good deal of time is spent studying polynomials in algebra courses that are intended to be
a preparation for the study of calculus. For the time being, we can consider polynomials to be
algebraic expressions such as
3x2 − 5x− 7 and x4 − 3x3 + 2x2 − 7. In algebra courses, we learned how to add, subtract, and multiply polynomials. We even studied
“polynomial long division” as a way to find a quotient and a remainder when one polynomial is
divided by another polynomial. This is similar to the work we have done with the integers and so it
may not be surprising that we will be able to develop our study of polynomials within the context
of ring theory.
