Unlike its more modern (and more expensive) cousin, the TI89, the TI83 Plus graphing calculator doesn't come with a builtin package to evaluate polynomials. In order to factor these equations, you need to download the appropriate piece of free software to your calculator.
Things You'll Need
 TI83
 TI Connectivity Kit

Connect the USB cord in the TI Connectivity Kit from your calculator to the computer.

Go to the TI83 downloads page (see Resources below) and doubleclick the "Factor Any Polynomial (Update)" link. Save the application to your desktop.

Drag the application file on your desktop and drop it onto the TI Connect icon on your desktop. This will automatically download the file to your calculator.

Press the "APPS" button on your TI83. Select "Factor Any Polynomial (Update)" by pressing the down tab and then "Enter."

Enter your polynomial function onto the screen and press "Enter." You will be given a list of factors.