Polarizability expressions are commonly used in optics and photonics to model light scattering by small particles. Models based on Taylor series of the scattering coefficients of the particles fail to predict the morphologic resonances hosted by dielectric particles. Here we propose to use the factorization of the special functions appearing in the expression of the Mie scattering coefficients to derive pointlike models. These models can be applied to reproduce both Mie resonances of dielectric particles and plasmonic resonances of metallic particles. They provide simple but robust tools to predict accurately the electric and magnetic Mie resonances in dielectric particles.