Properties of algebraic polynomials in one variable and their applications.

Abstract

The article studies the main properties of algebraic polynomials in one variable and their role in mathematical analysis. The concept of a polynomial, its degree, coefficients and roots are analyzed. The importance of polynomials in solving algebraic equations and their application in various mathematical and practical problems are also highlighted. The work studies the relationships between the algebraic concept of the polynomial ring K[X1...Xn] and the geometric concept of affine manifolds. A number of problems related to polynomial ideals and affine manifolds are presented: the problem of characterizing an ideal in the ring K[X1...Xn], the problem of solving polynomial equations with complete solutions. The results of the research demonstrate the important role of polynomial theory in algebra and mathematical analysis and substantiate their scientific and practical significance.