This document proposes a general factorization framework (GFF) for context-aware recommendation that takes a preference model as input and computes latent feature matrices for different context dimensions. GFF allows for easy experimentation with various linear models on both explicit and implicit feedback recommendation tasks involving multiple context dimensions. The document demonstrates GFF's potential by exploring different preference models on a 4-dimensional context problem using real-world implicit feedback datasets, showing that proper preference modeling significantly improves accuracy and previously unused models outperform traditional ones. GFF is also extended to incorporate additional information like item metadata, social networks and session data beyond just context.