Spectral indices such as NDVI have driven vegetation monitoring for decades, yet their design remains largely manual and ad hoc. Their usefulness stems not only from their empirical performance, but also from algebraic forms that remain compact and biologically interpretable. However, the space of possible algebraic expressions relating spectral bands is effectively infinite, making systematic search impractical without structural constraints. We introduce the Spectral Feature Polynomial (SFP) framework, a general pipeline that automatically discovers compact, interpretable spectral indices from labeled multispectral imagery. SFP constructs a library of ratio-based spectral features that inherit illumination invariance by construction. It then applies cross-validated feature selection and continuous coefficient optimization to produce a single closed-form equation per task, transparent to domain experts and deployable on any remote sensing platform without requiring standardization statistics. We validate the framework on two agricultural applications. For Kochia (Bassia scoparia) detection in Sentinel-2 imagery near Lucky Lake of Saskatchewan over three growing seasons, the same two-term equation emerged in 44 of 46 independent cross-validation folds, achieving 98.6% mean accuracy, more than 4 percentage points above the best established index under year-held-out evaluation. For wheat plant classification from UAV multispectral imagery, stage-specific indices achieved 99.5%, 97.2%, and 93.5% across three growth stages, compared to 78% or below for the best established index at late season when NIR-based contrasts lose discriminatory power as wheat senesces. In both applications, SFP yielded a single transparent equation that generalized across held-out regions and outperformed established indices.