The Fundamental Theorem of Algebra

This lecture introduces the fundamental theorem of algebra, which states that every polynomial of degree n has n complex roots. The theorem is explained through various examples and proofs, showing how to find the roots of a polynomial and represent it in terms of its factors. The lecture also covers the case of real polynomials, where complex conjugate roots are discussed. Additionally, it explores the factorization of real polynomials into linear and quadratic factors. The instructor emphasizes the significance of the theorem in understanding the roots of polynomials and their representation in the complex plane.