Factoring the GCF of a polynomial
First we learn to factor out the GCF of a polynomial. Here’s a video with some examples.
If you need more practice with that, here’s a worksheet with a bunch of problems along with the answers to check against.
Factoring a quadrinomial by grouping
Now we learn a method of factoring some four term polynomials by grouping the first two terms and the last two terms, and then finding the GCF of those groups. We finish by finding the GCF of the two terms that remain. Here’s a video that covers an example of this.
If you need more practice factoring a four term polynomial by grouping, here is a worksheet along with the key you can practice with.
Factoring a trinomial by grouping
Finally, we learned a generalized method of factoring trinomials of the form 
, finding two numbers that multiply to 
and add up to 
, and using those to rewrite a trinomial as a quadrinomial (4 term polynomial) so we could use factor by grouping. Here’s a video covering the “muggle way”, if you want more examples.
And finally here is a worksheet with a bunch of trinomials you can practice factoring using any method you’d like.