Factorization of the quintic x5+ x + n

• Main Authors: Soriano, Sonia B., Tan, Rachelle A.
• Format: text
• Language: English
• Published: Animo Repository 1993
• Subjects: Factorization of operators; Equations, Quintic; Factors (Algebra); Polynomials
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16114
• Institution: De La Salle University

This thesis presents a factorization of a special quintic x5 + x + n, where n is an integer, as a product of a quadratic polynomial and a cubic polynomial.In the article The Factorization of x5 + x + n found in Mathematics Magazine, Stanley Rabinowitz presents a solution for finding n for which the said quintic is reducible. The solution shows that +1, +6, +15, +22440, and +2759640 are the only integers for which such polynomial factors into the product of an irreducible quadratic and cubic polynomial. The researchers give a comprehensive algebraic solution in the factorization of the quintic x5 + x + n and include the details in the discussion and the proofs of the theorems which the author of the above-mentioned article failed to provide.