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Polynomials are widely employed to represent numbers derived from mathematical operations in nearly all areas of mathematics. The ability to factor polynomials entirely into linear components allows for a wide range of problem simplifications. This paper presents and demonstrates a novel straightforward approach to solving polynomial problems by converting them to matrix equations. Each polynomial of degree n can be decomposed into a sum of degree⌈ n 2⌉ polynomials squared, ie,∑ i= 0 n a i x i=∑ i= 1⌈ n 2⌉+ 1∑ j= 0 j=⌈ n 2⌉ b i, j x j 2. It follows that the complexity of factorizing a polynomial of degree 2 n is equivalent to that of factorizing polynomial of degree 2 n− 1. The proposed method for solving fourth-degree polynomials will be a valuable contribution to linear algebra due to its simplicity compared to the current method. This work presents a unique approach to solving polynomials of four or fewer …