Abstract <p>The triangular quantum well is selected as the theoretical model, and the Pekar variational method is adopted to handle the electron-phonon interaction. The inversion asymmetry inherent in the triangular quantum well structure lifts the electron spin degeneracy, thereby inducing the Rashba spin-orbit splitting of polaron energy levels and further forming two states with distinct energies. The energy splitting increases with the enhancement of the electron-phonon coupling strength, Coulomb binding potential strength, electron areal density, and Rashba coefficient. The ratio of the Rashba spin-splitting energy to the zero-spin ground state energies of polarons and electrons changes notably with variations in the wave vector, Coulomb binding potential strength, and electron areal density. Phonons make a negative contribution to the total energy of polarons, and their presence lowers the total energy of the particles. Consequently, the polaron splitting energy is more stable than that of bare electrons owing to the existence of phonons.</p>