ABSTRACT
Polynomials in one variable of arbitrary degree are the subject of this chapter whereas the theory of polynomials in two or three variables of degree. Polynomials form a particularly simple and useful class of functions. For example, complicated functions can often be approximated by polynomial ones. They also have important applications in matrix theory. Any real polynomial is equal to a real number times a product of monic real linear and monic irreducible real quadratic factors. This result is the basis of the method of partial fractions used in integrating rational functions in calculus. A radical expression is an explicit description of a complex number in terms of algebraic operations applied to the rationals. The remainder theorem for the integers leads to Euclid's algorithm for computing greatest common divisors of integers. In exactly the same way, the remainder theorem for polynomials leads to Euclid's algorithm for computing greatest common divisors of polynomials.
