There’s only one thing I don’t like about this method. It has one step which isn’t intuitive, and makes it all seem like magic.
When you have a coefficient in front of the term that isn’t one, you have to divide the factors by that number. And then you do “bottoms up” where the gets converted to . I don’t like that you have to randomly divide by a number, nor that the implicit implication is that .
A fellow math teacher at my school taught me to teach a very similar method, but that uses factor by grouping.
Given a quadratic, the first part is the same:
Rewrite the as (numbers from the diamond above)
Then the problem becomes a “factor by grouping” problem. You group the first two terms and second two terms and factor:
Then you see each term has an so you factor that out and are left with :
It might seem a little more complicated, because you have to factor a few times. But my kids tend to get it after practicing 3 or 4 problems, and it doesn’t involve any knowledge they didn’t already possess. They understand that and they understand how to factor . There is no lingering “why?”
 You could write it also and it would work. .