Publication Date: May, 2023
By: Samir Brahim Belhaouari ; Mohamad Hassan Fadi Hijab ; Zarina Oflaz
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 square.
It follows that the complexity of factorizing a polynomial of degree 2n is equivalent
to that of a factorizing polynomial of degree 2n − 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 degrees and presents new possibilities for tackling
larger degrees. Additionally, our methodology can also be used for educational purposes.
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Citation:
Belhaouari, S. B., Hijab, M. H. F., & Oflaz, Z. (2023). Matrix approach to solve polynomial equations. Results in Applied Mathematics, 18, 100368.