Divisibility of Trinomials by Irreducible Polynomials over F2

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Irreducible trinomials of given degree n over F₂ 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 F₂. A condition for divisibility of self-reciprocal trinomials by irreducible polynomials over F₂ is established. And we extend Welch's criterion for testing if an irreducible polynomial divides trinomials xᵐ+xˢ+1 to the trinomials xam+xbs+1.