In the recent paper arXiv:0710.4085 was shown that any solution of so called
polynomial moment problem, which asks to describe polynomials Q orthogonal to
all powers of a given polynomial P on a segment, may be obtained as a sum of
some "reducible" solutions related to "compositional right factors" of P.
However, the methods of arXiv:0710.4085 do not permit to estimate the number of
necessary reducible solutions and their explicit form. In this paper we prove a
version of the "second Ritt theorem" about polynomial solutions of the
functional equation A(C)=B(D) for the functional equation A(C)=B(D)=E(F) and on
this base show that any solution of the polynomial moment problem may be
obtained as a sum of at most two reducible solutions. We also describe these
solutions in a very explicit form.