Very recently the ZOOM 200 and ZOOM 300 programs of TI-84 plus graphing calculators were banned because they were literally doing all of the work for students. So no longer can students count on this advanced program to do all of the dirty work for them when it comes to factoring polynomials; however, there are still certainly technology shortcuts that students can take if they know a little about both their graphing calculator and solving polynomials.
To begin with, students should make sure the function they are working with is either solved for y or set equal to zero (either will do in this case). After this step, they can put their function in the Y= portion of the calculator. This button is located in the northwest most corner of either your TI-83 or TI-84 device. Make sure every other line is cleared now, except for your current problem. After you input your equation, then you can go to the built in table of values that can be found under the GRAPH button (just hit the 2nd key before you hit the GRAPH key). This will give you a complete list of what the y value of your equation would be depending on the x value.
If the solutions or roots of your given equation are integers and are relatively small, then it should not take long scrolling through the endless table to find where y is equal to zero. When y is equal to zero this means you have found the x values that are considered solutions to the equation. Let’s say we have found a zero at both x =2 and x = -1. If those are solutions, then this means the factors of your equation would be (x-2) and (x + 1). Granted, this method generally only works when the solutions are integers but more times than not on an Algebra, that is what you will find to be the case. This method is a good primary way to do the problem, then you can easily check it by hand. Simply, multiply your factors together and this should yield you the original equation that you started with.