Algebra

Abstract

Introduction. In the chapter Algebra, many problems can be treated using the properties of arithmetic or geometric progressions. There are several problems about finding a sum or a product. The majority of equations or system of equations can be treated by algebraic transformations, by the method of estimation or by using relation between arithmetic mean and geometric mean. There are many problems devoted to polynomials. In some of these problems, one needs to find the roots of a polynomial with integer coefficients. In particular, the following statement is used: if the leading coefficient of a polynomial is equal to 1, then the rational roots of this polynomial are integers. For the readers convenience, we list and provide the formulations of all used theorems and proof techniques that are outside of the scope of the regular school program.