# Polynomial Function

1. Introduction

A polynomial function is a function such as a quadratic, a cubic, a quadratic, and so on, involving

only non-negative integer powers of x. We can give a general definition of a polynomial, and

define its degree.

2. What is a polynomial?

A polynomial of degree n is a function of the form

f(x) = anxn + an−1xn−1 + . . . + a2x2 + a1x + a0

where the a’s are real numbers (sometimes called the coefficients of the polynomial). Although

this general formula might look quite complicated, particular examples are much simpler. For

example,

f(x) = 4x3

− 3x2 + 2

is a polynomial of degree 3, as 3 is the highest power of x in the formula. This is called a cubic

polynomial, or just a cubic. And

f(x) = x7

− 4x5 + 1

is a polynomial of degree 7, as 7 is the highest power of x. Notice here that we don’t need every

power of x up to 7: we need to know only the highest power of x to find out the degree. An

example of a kind you may be familiar with is

f(x) = 4x2

− 2x − 4

which is a polynomial of degree 2, as 2 is the highest power of x. This is called a quadratic.

Functions containing other operations, such as square roots, are not polynomials. For example,

f(x) = 4x3 + px − 1

is not a polynomial as it contains a square root. And

f(x) = 5x4

− 2x2 + 3/x

is not a polynomial as it contains a ‘divide by x’.

Please watch the fallowing video to reach a better understanding of Polynomial Function: