Factoring Trinomials.

I have been trying to find a way to clarify factoring trinomials with a leading coefficient of other than one.  When I first learned it, you had factor the leading coefficient and the constant, figure out which set of factors you needed before finally finding the answer.  It took quite a bit of time and frustration.

Several years later, I learned to use the diamond with the product at the top and sum at the bottom to find the factors.  It worked well but my high school students often could not relate the numbers in the diamond when rewriting the equation into four terms.  The other day, I saw a video which used the diamond method but with a slight difference.

When he wrote the product, he included the x^2 and when writing factors, he wrote it with the x instead of just the coefficients.

This was so much clearer because anyone could see the relationships and its much easier to see where the factoring terms go.  I showed a write-up with a few more steps of what the person showed.  I had the students take notes from the video with added steps and comments.

Today when we worked the first problem, together.  I insisted they look at their notes while we worked the problem.  I am taking steps to make them more independent learners and this includes learning to look and follow their notes.

One of my students said this way was better because it reminded him to include all the variables.  I think I'll be teaching it this way.  Let me know if you have a good way to teach this topic.