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The Trinomial Sextic Equation, its Algebraic Solution by Conversion to Solvable Factorized Form

Samuel Bonaya Buya

In this research the basis is established for solvability of the Galois group of a degree n polynomial. We establish that higher degree polynomials can in general be reduced to lower degree solvable forms. The lower degree root forms are then converted to higher degree form through conversion to what was identified as the nth order algebraic form of a root. Upon the basis of findings on solvability of higher degree polynomials a factorization method of solving higher degree polynomials is established.

We present a method of solving the sextic equation by converting it to a solvable factorized form. The factorized form will consist of two auxiliary cubic equations and their five parameters. The factorized form is selected such that four of its parameters are functionally related to the two parameters of the reduced sextic equation. The fifth parameter will be an identified rational number