  We present a few factorizations of polynomials over finite fields. These
factorizations are related to traces, compositions of polynomials and binomial
coefficients. As a corollary we obtain a description of all irreducible
polynomials $Q\in {\mathbb F}\_2[x]$ such that $Q(1+x+x^2)$ (or $Q(x+x^2)$)
remain irreducible.
