A polynomial is an expression of one variable in the form *a*_{n}*x*^{n} + *a*_{n-1}*x*^{n-1} + ^{ ... } + *a*_{2}*x*^{2} + *a*_{1}*x* + *a*_{0}, where *a*_{0}, *a*_{1},…, *a*_{n} are
real numbers with *a*_{n}≠ 0 and *n* is a positive integer. Many real-life
situations are easily modeled by polynomial functions. Some of the most
familiar are quadratic functions, which are
functions of the form *f* (*x*) = *ax*^{2} + *bx* + *c*.
Other polynomial functions are also commonly seen in mathematical models. In
the following sections we'll study the general form of polynomials, what a
polynomial function looks like, and how to find the roots of a given
polynomial function. The roots of a polynomial function are the values of *x*
for which the function equals zero. In a related topic, we'll take a look at
rational functions, which are functions that can be written as a quotient of
two polynomials. After an in-depth look at polynomial functions, they will be
easy to deal with in calculus.