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