Polynomial as a mathematical expression made up of more than one term, where each term has a form of axn (for constant a and none negative integer n). For example: 2x3.
In polynomial function the input is raised to second power or higher. The degree of a polynomial function is defined as its highest exponent.
Even degree polynomial function has an even highest exponent (2, 4, 6, etc.).
Odd degree polynomial function has an odd highest exponent greater than 1 (3, 5, 7, etc.).
For example: The function f(x)=x3+3x2-x-3 is a third degree polynomial function (in this function the highest exponent is 3), it is an odd degree function (the highest exponent 3 is odd).
The factored form of a polynomial function shows the x intercepts of the function.
The standard form of the polynomial function shows the y intercept of the function.
The end behavior shows the location of the graph of the function for very small and very large values of x. To know the end behavior of a polynomial function we need to look at its highest exponent (if it is odd or even) and the sign of its coefficient.
The polynomial remainder theorem says that when we divide a polynomial function f(x) by the expression x-a the remainder is f(a). Therefore, to find the remainder we do not need to do the division, we just plug x=a into f(x) and calculate the output.
Note that polynomial is written in descending order of its exponents.
Quadratic functions are the simplest form of polynomial functions (they have an exponent of 2). Quadratic functions topic is divided into two pages: quadratic equations and quadratic functions and graphing quadratic functions.
Another topic that you should know before learning about polynomial functions is exponential expressions topic, since it explains the rules and the operations with exponents.
Continue reading this page for detailed explanations and examples.