The Casas–Alvero conjecture predicts that every univariate polynomial over a field of characteristic zero having a common factor with each of its derivatives H_i (f ) is a power of a linear polynomial. One approach to proving the conjecture is to first prove it for polynomials of some small degree d, compile a list of bad primes for that degree (namely, those primes p for which the conjecture fails in degree d and characteristic p) and then deduce the conjecture for all degrees of the form d_pℓ , ℓ ∈ N, where p is a good prime for d. In this paper we calculate certain distinguished monomials appearing in the resultant R(f, H_i (f )). As a corollary, we obtain a (non-exhaustive) list of bad primes for every degree d ∈ N \ {0}.