  We factor the virtual Poincare polynomial of every homogeneous space G/H,
where G is a complex connected linear algebraic group and H is an algebraic
subgroup, as $t^{2u} (t^2-1)^r Q_{G/H}(t^2)$ for a polynomial $Q_{G/H}$ with
non-negative integer coefficients. Moreover, we show that $Q_{G/H}(t^2)$
divides the virtual Poincar\'e polynomial of every regular embedding of G/H, if
H is connected.
