All polynomials considered in this paper belong to ℚ[x] and reducibility means reducibility over ℚ. It has been established by one of us  that every binomial in ℚ[x] has an irreducible factor which is either a binomial or a trinomial. He has further raised the question “Does there exist an absolute constant K such that every trinomial in ℚ[x] has a factor irreducible over ℚ which has at most K terms (i.e. K non-zero coefficients)?”
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