Functor calculus uses the intuition of calculus to approximate functors between categories by simpler functors. One such type of simpler functors are the "linear" functors. Linear functors are simple because they are determined in a weak sense by their coefficient spectra. A reduced homotopy functor is "linear" if it takes homotopy pushout squares to homotopy pullback squares. As we can extend the notion of linear to the notion to being homogenous of degree n, and this gives a better approximation, we generalize to "polynomial" functors by using n-cubes instead of squares, and this gives a better approximation to the functor. Then, in analogy with Taylor expansions, we can construct a resolution of the functor by a series of functors, $P_n$ where each $P_n$ is n-homogenous. One application of this construction is to Waldhausen K- theory, from which the derivative gives Topological Hochschild homology.