We report the results of variational calculations of elastic electron scattering by tetrafluoroethene, C_2F_4, with incident electron energies ranging from 0.5 to 20 eV, using the complex Kohn method and effective core potentials. These are the first fully \ai calculations to reproduce experimental angular differential cross sections at energies below 10 eV. Low-energy electron scattering by C_2F_4 is sensitive to the inclusion of electronic correlation and target-distortion effects. We therefore present results that describe thedynamic polarization of the target by the incident electron. The calculated cross sections are compared with recent experimental measurements.