This paper presents a technique for making the evaluation of POD models with polynomial nonlinearities less intensive. Regularly, Proper Orthogonal Decomposition (POD) and Galerkin projection have been employed to reduce the high-dimensionality of the discretized systems used to approximate Partial Differential Equations (PDEs). Although a large model-order reduction can be obtained with these techniques, the computational saving during simulation is small when we have to deal with nonlinear or Linear Time Variant (LTV) models. In this paper, we present a method that exploits the polynomial nature of POD models derived from input-affine high-dimensional systems with polynomial nonlinearities, for generating compact and efficient representations that can be evaluated much faster. Furthermore, we show how the use of the feature selection techniques can lead to a significant computational saving.