I have created a Mathematica object that people can use to practice factoring trinomials the “best” way. It is a CDF file (computable document file) and requires a CDF plug-in which can be found here. Once you have the plug-in you can go to Mathematics‘ demonstration site here and browse through wondrous mathematical demos.
The trinomial practice object is located here. Sometimes it stops working for unknown reasons. All I can say is reload and start again.
As you work through the problems, you will see that the method generalizes beautifully. For instance, if you are factoring , you might not notice the greatest common factor of . If this was factored out, the trinomial would be easier to factor, but the method doesn’t care. Here is the example worked out.
A factoring problem that gives students trouble is something like this . Append a zero and using the “best” factoring method as done in the example.
And finally what if we had to factor . It is already factored and the “best” factoring knows it as in this example.
The “best” way to factor trinomials is fun to learn and very useful. Give it a try.