Coefficients for a Power Series Expansion is given by the formula:

Basic Taylor Polynomials yield the following Basic Taylor Series at  x = 0.  The Taylor Series at  x = 0 are also called Maclaurin series.

The La Grange Formula: 

REMEMBER:
The degree of a Taylor polynomial is whatever the highest x power is.
The order of a Taylor polynomial is dependent on how many terms there are.