We show how one can construct a simple exchange functional by extending the well-know local-density approximation (LDA) to finite uniform electron gases. This new generalized local-density approximation functional uses only two quantities: the electron density ρ and the curvature of the Fermi hole α. This alternative "rung 2" functional can be easily coupled with generalized-gradient approximation (GGA) functionals to form a new family of "rung 3" meta-GGA (MGGA) functionals that we have named factorizable MGGAs. Comparisons are made with various LDA, GGA, and MGGA functionals for atoms and molecules.