  We predict a p-wave Cooper pairing of the spin-polarized fermions in a binary
fermion-boson mixture due to the exchange of density fluctuations of the
bosonic medium. We then examine the dependence of the Cooper paring temperature
on the parameters of the system. We finally estimate the effect of combining
the boson-induced interaction with other pairing mechanisms, e.g the
Kohn-Luttinger one, and find that the critical temperature of p-wave Cooper
pairing can be realistic for experiment.
