Abstract: Abstract. We prove a necessary and sufficient condition on the list of nonzero integers u1…, uk, k≥2, under which a monic polynomial f∊ 2 ℤ [ x ] is expressible by a linear form u 1 f 1 + … + u k f k in monic polynomials f 1 …f k ∊ ℤ[x]. This condition is independent of f . We also show that if this condition holds, then the monic polynomials f 1 , … f k can be chosen to be irreducible in ℤ[x].