In this lesson various problems related to roots, polynomial equations, and irreducibility of polynomials are discussed. A major tool in most of the problems is the usage of complex numbers.
The lesson starts with some warming-up problems for finding roots. These problems can be solved with brute force, or with more elegant technique using that the polynomials have special properties (e.g. reciprocity). The second part of the lesson focuses on division of polynomials and related topics. The last part is devoted to polynomial equations and irreducibility, where both division and complex numbers technique have to be applied. The level of the lesson gradually increases and at the end, some challenging problems from national competitions are included.