  A polynomial $p\in\mathbb{R}[x]$ is a divisor of some polynomial $0\neq
f\in\mathbb{R}[x]$ with non-negative coefficients if and only if $p$ does not
have a positive real root. The lowest possible degree of such $f$ for a given
$p$ is known for quadratic polynomials. We provide it for cubic polynomials and
improve known bounds of this value for a general polynomial.
