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.