INVESTIGATION OF THE SOLUBILITY BY RADICALS OF A SELECTED TRINOMIAL OF HIGHER ORDER (DEGREE 5 n 7) POLYNOMIALS USING GALOIS THEORY

This dissertation extends the results of the work of Galois and his contribution to the development of modern algebra. The fact is that polynomials of higher degree (n 5) are not solvable by radicals. However, very few at that were later discovered to be solvable by radicals. In particular, we specifically identified some special polynomials which are irreducible but can be solve by radicals. These polynomials are in trinomial form ( ).Then using the quintic, sextic, and septic polynomial as case study, we finally deduced that such type of a trinomial polynomial can be generalized and a theorem was then put forward to support our argument