We give explicit bounds for the absolute values of the coefficients of the divisors of a complex polynomial. They are expressed in function of the coefficients and of upper and lower bounds for the roots. These bounds are compared with other estimates, in particular with the inequality of Beauzamy [B. Beauzamy, Products of polynomials and a priori estimates for coefficients in polynomial decompositions: A sharp result, J. Symbolic Computation, 13, 463 - 472 (1992)]. Through examples it is proved that for some cases our evaluations give better upper limits.
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