# Basic knowledge of polynomial functions

A polynomial is a mathematical expression constructed with constants and variables using the four operations:

 Polynomial Example Degree Constant 1 0 Linear 2x+1 1 Quadratic 3x2+2x+1 2 Cubic 4x3+3x2+2x+1 3 Quartic 5x4+4x3+3x2+2 x+1 4

In other words, we have been calculating with various polynomials all along. When two polynomials are divided it is called a rational expression.

In such cases you must be careful that the denominator does not equal zero. Division by zero is not defined and thus x may not have a value that allows the denominator to become zero. Otherwise, any other value may be substituted for x.

Example

$\frac{x^{3}-x}{6-x}$

x must not have the value of 6 since 6-6=0.

## Video lesson

Of what degree is the given equation

$f(x)=\frac{x^{5}-x}{x}+x^{2}$