In this paper two theoretical methodologies, the Schwinger multichannel (SMC) method and the independent atom model with the screening corrected additivity rule (IAM-SCAR), were employed to study positron scattering by benzene over a broad impact energy range. The SMC calculations were carried out in the static plus polarization approximation, accounting for the elastic channel, for impact energies up to 20 eV. The IAM-SCAR method covered energies up to 1000 eV to provide total, elastic, ionization, excitation, and positronium formation cross sections. In the low-energy region we discuss how the description of the polarization effects affects the cross sections. In particular, our calculations support the existence of a bound state in the positron scattering by benzene, in agreement with previous predictions by Young and Surko [Phys. Rev. A 77, 052704 (2008)NIMBEU0168-583X10.1103/PhysRevA.77.052704].