  We have carried out a spectropolarimetric search for hidden broad-line
quasars in three ultraluminous infrared galaxies (ULIRGs) discovered in the
positional correlations between sources detected in deep radio surveys and the
IRAS Faint Source Catalog. Only the high-ionization Seyfert 2 galaxy TF
J1736+1122 is highly polarized, displaying a broad-line spectrum visible in
polarized light. The other two objects, TF J1020+6436 and FF J1614+3234,
display spectra dominated by a population of young (A-type) stars similar to
those of ``E + A'' galaxies. They are unpolarized, showing no sign of hidden
broad-line regions. The presence of young starburst components in all three
galaxies indicates that the ULIRG phenomenon encompasses both AGN and starburst
activity, but the most energetic ULIRGs do not necessarily harbor ``buried
quasars''.
  We find that a luminous infrared galaxy is most likely to host an obscured
quasar if it exhibits a high-ionization ([O III] 5007/Hb >~ 5) spectrum typical
of a ``classic'' Seyfert 2 galaxy with little or no Balmer absorption lines, is
``ultraluminous'' (L_IR >~ 10^12 L_sun), and has a ``warm'' IR color (f_25/f_60
>~ 0.25). The detection of hidden quasars in this group but not in the
low-ionization, starburst-dominated ULIRGs (classified as LINERs or H II
galaxies) may indicate an evolutionary connection, with the latter being found
in younger systems.
