HOW MANY SOLUTIONS DOESx2+ 1 = 0 HAVE? AN ABSTRACT ALGEBRA PROJECT

This paper describes both the implementation and the mathematics of an Abstract Algebra project. The project begins with a seemingly simple question about a polynomial equation. It provides a concrete setting for exploring the relationships between polynomials, matrices, modular arithmetic, unique factorization, roots of unity, and order of group elements to help students understand the underlying abstract ring, field, and group theory.