We present spectropolarimetric observations of a sample of three quasars selected because of their very different broad-band polarization properties. All of the objects in the sample show frequency-dependent polarization degree (FDP), and two of them also show frequency-dependent polarization position angle (FDPA). We have not detected polarization in the spectral emission lines in any object of the sample, although the possibility exists that the iron blends in CTA 102 may be polarized. Our observations show important differences between the three objects. While 3C 273 has been previously discussed in terms of a multiple synchrotron source model, a conclusion supported by our results, this seems not to be the case for 3C 345. We examine a number of processes capable of generating the observed FDP and FDPA of this object. A combination of a nonthermal source and scattering from dust or gas in the local interstellar medium can explain our observations, although some restrictions must be imposed to avoid polarization of the spectral emission lines. The quasar CTA 102 shows a very complex wavelength-dependent polarization, which may be related to the iron blends in the spectrum. We also present a statistical test developed by us to examine the possible polarization of the lines.