Eisenstein's Criterion: An Intuitive explanation for an intriguing topic

This article introduces irreducible polynomials over the rationals and how Eisenstein's Criterion can be used to prove irreducibility. Starting with a comparison between reducible and irreducible with simple analogies, then explaining how to factor a polynomial over Q. Later showing examples of polynomials that failed to meet the criteria to fulfill Eisenstein's Criterion, and why the divisibility criteria matters. With worked examples this article shows why the criterion is sufficient but not necessary for a polynomial to be irreducible. By the end of the article, readers should have a good understanding of Eisenstein's Criterion and should be able to apply it,