A new computational approach has been used to evaluate the rotationally summed, vibronically elastic integral cross sections from the scattering of slow electrons (energy ranging from 1.0 eV up to 40.0 eV) by tetrafluoromethane molecules in the gas phase. The various symmetry components have been analyzed using the exact static exchange approximation and also by including a nonempirical, model polarization potential employed before by our group. A comparison with earlier calculations and with existing experiments allows us to assign the symmetries of the shape resonances in the 5-30 eV energy region which are seen by experiments and are also shown by the present calculations.