Raised the differential method of resolving rational function into fractions, and formulas were suggested of the coefficients which correspond to liner factor and quadratic prime factor.

Method and theoretcial basis of finding out all linear power integer factors with the rational root of the existing integer coefficient unury multinomial being given and simple and easy way of analyzing the fourth power multinomial without the rational root being shown.

In this thesis, the concepts of first reason of fault and non exact subfrequencyand non exact multifreqnency (subfrequency hysteresis.

It is obtained a sufficient and necessary condition on x~n-bx-a having a irreducible quadratic factorization x~2-sx-t in Q based on the recurrence, founded a relation between the coefficients a and b of x~n-bx-.

 Using Baker methods, it is proved that if x n-x-a has quadratic factorization, then n<512 880, except that case n≡2(mod6) and a=-1.

In this aper, Using Baker methods, we prove that if x n-x-a has quadratic factorizations, then n <512880, except case n ≡2(mod6) and a=-1.

In this paper,using the Baker method,we prove that if the trinomi a l x-n-x-a has a quadratic factor over Q,then n<512880 ex cept when n≡2(mod 6) and a=-1.