  Irreducible trinomials of given degree n over $F_2$ do not always exist and
in the cases that there is no irreducible trinomial of degree n it may be
effective to use trinomials with an irreducible factor of degree n. In this
paper we consider some conditions under which irreducible polynomials divide
trinomials over $F_2$. A condition for divisibility of self-reciprocal
trinomials by irreducible polynomials over $F_2$ is established. And we extend
Welch's criterion for testing if an irreducible polynomial divides trinomials
$x^m+x^s+1$ to the trinomials $x^{am}+x^{bs}+1$.
