The anatomy of a polynomial

In our study of algebra we first learn how to factorise x^n-1 but we only factorise it once. For example when n=2 we have the difference of two squares and so on. In this course we give a complete factorisation by proving that the cyclotomic polynomials are irreducible. This topic I only learned when I was in graduate school but should really be part of a high schooler's foundation and as has been demonstrated by my students it can be learned by students in grade 11 without difficulty if they have had some exposure to proofs possibly through math olympiad.