Explore a crucial theorem in abstract algebra demonstrating that the polynomial ring over a unique factorization domain (UFD) is also a UFD. Delve into key concepts such as the content of a polynomial and Gauss' lemma. Examine the proof that polynomials factoring over the field of fractions of an integral domain also factor over the integral domain itself. Follow along as the instructor methodically introduces the topic, presents Gauss' lemma, and guides you through the limits and proof of this fundamental result in ring theory.