A Framework for Factoring and Counting certain Polynomials over Finite Fields

The purpose of this talk is to present a method that can be used to provide factorizations of certain classes of polynomials with some applications to counting irreducible polynomials of corresponding types. For example, the factorization of x (q 1) 2 1 has a form similar to the factor- ization of x q 1 1 over Fq. It is also useful in counting monic irreducible polynomials of the form p(x r ) where p(x) 2 Fq(x) has degree m.