A cyclotomic polynomial φk(x) is an essential cyclotomic factor of f (x) ∈ Z[x] if φk(x) ∥ f (x) and every prime divisor of k is less than or equal to the number of terms of f: We show that if a monic polynomial with coefficients from {-1, 0, 1} has a cyclotomic factor, then it has an essential cyclotomic factor. We use this result to prove a conjecture posed by Mercer ['Newman polynomials, reducibility, and roots on the unit circle', Integers 12(4) (2012), 503-519]. © 2019 Australian Mathematical Publishing Association Inc.