A new method of finding the algebraic solution of the degree n polynomial Samuel Bonaya Buya 17/4/2025 Contents Introduction 2 Algebraic solution of the degree n polynomial step by step approach 3 Rewriting the Final Root Expression ............. 6 Further analysis ......................... 6 Conclusion 8 COPE Compliance and AI Use Disclosure 9 Zero plot 9 Abstract This paper introduces a novel algebraic method for solving the tri- nomial polynomial equation of the form   ++=0 , where ,  ∈ ℂ and ∈ℕ , >2 . Traditional approaches to such polynomials are often limited due to their irreducibility and non-solvability by rad- icals for higher degrees. We propose a solution based on a fac- torization identity involving symmetric expressions of the form   2 ± √ − , which enables a reduction to a quadratic in an auxil- iary parameter  . This framework results in an explicit closed- form expression for roots in terms of  ,  , and  , leveraging symmetry, complex conjugation, and roots of unity. The method extends the known boundaries of solvability for non-quadratic 1