Conceptual complexity is emerging as a new bottleneck as datarbase developers, application developers, and database administrators struggle to design and comprehend large, complex schemas. The simplicity and conciseness of a schema depends critically on the idioms available to express the schema. We propose a formal conceptual schema representation language that combines different design formalisms, and allows schema manipulation that exposes the strengths of each of these formalisms. We demonstrate how the schema factorization framework can be used to generate relational, object-oriented, and faceted physical schemas, allowing a wider exploration of physical schema alternatives than trar ditional methodologies. We illustrate the potential practical benefits of schema factorization by showing that simple heuristics can significantly reduce the size of a real-world schema description. We also propose the use of schema polynomials to model and derive alternative representations for complex relationships with constraints.