How I Teach Factoring Quadratics


Using this method to teach factoring quadratics has helped my algebra students so much!  There are no tricks! This works with any lesson and is easy for teachers too.

I know of a few different methods people use to teach factoring, but I’ve never been a fan of the “fancy” methods.  They just don’t work for me.  When I teach factoring, I actually teach the unit backward.  I teach factoring by grouping, factoring trinomials when a≠1, factoring trinomials when a=1, then special cases.

I start with factoring by grouping, because once students can do that, factoring trinomials is easy.  I tend to spend an extra day teaching factoring by grouping.  When students have that down, I move on to factoring trinomials.  I prefer teaching when a≠1 first, because when a=1 is really just a special case.  If students can handle the “harder” version, there almost isn’t a need to teach the “easier” version.
So, this is how I teach factoring.  This is not revolutionary.  It is not new, or even interesting.  But it works, every time.  I've often heard this method called "splitting the middle".

First, I have students multiply the “a” value by the “c” value.

How I Teach Factoring Quadratics
Then, I tell them they are looking for two numbers that multiply to that value.  I have them make a list.

How I Teach Factoring Quadratics

Only after that do I have them find the pair of numbers that adds to the “b” value.

How I Teach Factoring Quadratics

Next, I have students split the middle and finish by factoring by grouping.  So, example student work for the example would look like this:

How I Teach Factoring Quadratics

I prefer to teach factoring this way because it doesn’t rely on tricks and it works every time.  Also, after this lesson, teaching a=1 is just a special case.

In my TpT store, I have a full unit with activities to teach polynomials and factoring.  The unit includes guided notes, worksheets, warm-ups, activities, and other materials to effectively teach your students. Click to find my Polynomials and Factoring Unit.



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