  The hard-gluonic contribution to the first moment of the polarized proton
structure function $g_1^p(x)$ is dependent of the factorization convention
chosen in defining the quark spin density and the hard cross section for
photon-gluon scattering. Two extremes of interest, namely gauge-invariant and
chiral-invariant factorization schemes, are considered. We show that in order
to satisfy the positivity constraint for sea and gluon polarizations, the
polarized valence quark distributions should fully account for the observed
$g_1^p(x)$ at $x\gsim 0.2\,$. This together with the first-moment and
perturbative QCD constraints puts a pertinent restriction on the shape of
$\Delta u_v(x)$ and $\Delta d_v(x)$. The spin-dependent sea distribution in the
gauge-invariant factorization scheme is extracted from the data of $g_1^p(x)$.
It is shown in the chiral invariant scheme that it is possible to interpret the
$g_1^p(x)$ data with anomalous gluonic contributions, yet a best least $\chi^2$
fit to the data implies a gluon spin distribution which violates the positivity
condition $|\Delta G(x)|\leq G(x)$. We then propose a more realistic set of
parton spin distributions with sea polarization and with a moderate value of
$\Delta G$. The polarized parton distributions in this work are presented in
the next-to-leading order of QCD at the scale $Q^2=10\,{\rm GeV}^2\,$.
Predictions for the polarized structure functions $g_1^n(x)$ of the neutron and
$g_1^d(x)$ of the deuteron are given.
