1 - THE FOUNDATIONS OF ALGEBRA

Abstract

This chapter reviews some fundamentals of algebra and discusses the meaning and use of variables, algebraic expressions and polynomial forms, factoring, and operations with rational expressions or algebraic fractions. The rational and irrational numbers together form the real number system. In regard to the operations of addition and multiplication, the real number system has properties that are fundamental to algebra. There is a simple and very useful geometric interpretation of the real number system. The set of real numbers is identified with all possible points on a straight line and for every point on the line there is a real number and for every real number there is a point on the line. The line is called the real number line, and the number associated with a point is called its coordinate. A polynomial is an algebraic expression of a certain form, which plays an important role in the study of algebra, as many word problems translate into equations or inequalities that involve polynomials. The degree of the product of two nonzero polynomials is the sum of the degrees of the polynomials.