Polynomials. We define the -th power of by . A polynomial is of the form . Each of the polynomial is a term, and of the term is called a coefficient. In particular, the coefficient is called the leading coefficient of the polynomial if .
Factoring polynomials. In many cases we find by the method of ``trial and error'' that a polynomial of interest can be expressed as a product of polynomials of the form . Occasionally you may be able to use the factoring formula
Polynomial functions. A function is called a polynomial function of degree if
Synthetic division. Suppose that is the polynomial function (6), and that is any real number. By using the guidelines for synthetic division in page 234, we can always obtain the quotient
Remainder Theorem. The formula (7) implies that we obtain as the result of synthetic division. In particular, if and only if is a factor of , which we call factor theorem.
Zeros of polynomials. The zeros of a polynomial are the solutions of the equation . In particular, the polynomial (6) of degree has exactly zeros