Irreducible Polynomials: Degree and Roots

This lecture covers the concept of irreducible polynomials, focusing on their degree and roots. It explains the properties of irreducible polynomials in different fields, such as the cancellation property and the degree of the polynomial. The lecture also discusses examples of irreducible polynomials and their roots, including the Eisenstein criterion. Additionally, it explores the relationship between the degree of a polynomial and its roots, emphasizing the importance of understanding these concepts in algebraic structures.