You have been exploring numbers and the patterns they hide within them since your earliest school days. In what follows, we begin a process of abstraction, with the goal of understanding the consequences of the properties and patterns familiar from your work with the integers and polynomials. How far does our understanding of factorization in the integers stretch to other types of numbers and other mathematical objects (like polynomials)? In this chapter we will set the ground work for answering that question by introducing ideas that will assist us in streamlining our investigation into factorization.
