# 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 | 3x+2^{2}x+1 |
2 |

Cubic | 4x+3^{3}x+2^{2}x+1 |
3 |

Quartic | 5x+4^{4}x+3^{3}x+2 ^{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

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