This presentation introduces a two-dimensional representation of the space of quadratic trinomials, transforming how we can represent polynomial reducibility. Traditionally visualized in three dimensions, the space of quadratic trinomials is reimagined here with an equivalence relation that enables a simplified, two-dimensional representation. This approach reveals a distinct structural pattern: reducible quadratics occupy specific, predictable regions along certain lines within the space. With this visualization, we establish a straightforward method for generating reducible quadratics with integer coefficients directly, bypassing traditional tests for reducibility. By mapping these polynomials onto a two-dimensional plane, we provide a novel perspective on polynomial structure, offering both a practical and visual approach to understanding reducibility in quadratic trinomials.