1 - BASIC ALGEBRA

Abstract

Algebra is the systematic study of the operations of arithmetic and relations between numbers expressed by these operations. This chapter describes the features of algebra: brevity and generality. Algebraic notation is the shorthand of mathematics. It makes relations between numbers as short and as clear as possible. Their ability to abbreviate complicated ideas is an important feature of algebraic formulas. Their generality is also an important feature; formulas can express many facts in one statement. In working specific problems, the brevity and generality of algebra are exploited. The chapter discusses the properties of the common algebraic expressions, polynomials. Polynomials in several variables are sums. They are added, subtracted, and multiplied just like other sums. Factoring is the process of expressing a polynomial as a product of polynomials of lower degree. It is useful for simplifying algebraic expressions, for solving certain types of equations, and for numerical work. Quotients of polynomials are called rational expressions. A rational expression is in lowest terms if numerator and denominator have no common polynomial factors.