A Structural Linear Framework for Solving General Polynomial Equations

This work presents a novel and unified approach to solving general nth-degree polynomial equations by transforming them into an equivalent structured system of linear equations. Instead of relying on traditional algebraic factorization, numerical approximation, or case-by-case methods, the proposed framework introduces a systematic sequence of transformations that reduces the complexity of high-degree polynomials step by step. The method is built on a set of foundational theorems that connect polynomial coefficients to an associated linear structure, ultimately leading to a solvable nth-order linear equation. This approach aims to unify polynomial theory under a consistent algebraic mechanism, offering both theoretical insight and practical computation advantages. By bridging polynomial equations and linear algebra in a structured way, this framework provides a new perspective on classical algebraic problems and opens potential pathways for further generalization in higher mathematics.