Abstract
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∈F_2[x]
such that
Q(1+x+
x
2
)
(or
Q(x+
x
2
)
) remain irreducible.