  Gordon and McMahon defined a two-variable greedoid polynomial $ f(G;t,z) $
for any greedoid $ G $. They studied greedoid polynomials for greedoids
associated with rooted graphs and rooted digraphs. They proved that greedoid
polynomials of rooted digraphs have the multiplicative direct sum property. In
addition, these polynomials are divisible by $ 1 + z $ under certain
conditions. We compute the greedoid polynomials for all rooted digraphs up to
order six. A greedoid polynomial $ f(D) $ of a rooted digraph $ D $ of order $
n $ GM-factorises if $ f(D) = f(G) \cdot f(H) $ such that $ G $ and $ H $ are
rooted digraphs of order at most $ n $ and $ f(G),f(H) \ne 1 $. We study the
GM-factorability of greedoid polynomials of rooted digraphs, particularly those
that are not divisible by $ 1 + z $. We give some examples and an infinite
family of rooted digraphs that are not direct sums but their greedoid
polynomials GM-factorise.
