CHAPTER 3 - POLYNOMIAL FUNCTIONS

Abstract

This chapter focuses on polynomial functions. A polynomial is a function whose values are defined for all real x. The degree of a polynomial is the highest exponent occurring with nonzero coefficient. Polynomials play a central role in mathematics for a number of reasons: (1) they arise naturally in many applications; (2) their values can be computed using only the simplest operations of arithmetic—addition, subtraction, and multiplication; and (3) highly complicated functions can be closely approximated by polynomials. Numerical work with polynomials is perfectly suited for high speed computers. Polynomials combine by addition and by multiplication. To multiply two polynomials, each term is multiplied in the first factor by every term in the second factor. The reverse of multiplying is factoring, that is, expressing a polynomial as a product of other polynomials. There is no systematic procedure for factoring other than guesswork, testing, and familiarity with certain common identities. The chapter discusses zeros of higher degree polynomials.