I was pleasantly surprised to learn of this method after I had originally learned the "trial and check" method you described first. I learned of the AC method from a colleague. Later, I saw it described in a college algebra book. I had studied math for years before I learned of this alternative method. In the books where I've seen this method described, it is given as an alternative to the method I call trial and check.
In my experience, it is not such a popular way to factor with students, mostly because it involves more steps. (The trial and error may take longer but it is easier to remember.) Also, most of the students (in my experience) do not have many problems that are more easily factored using the AC method.
The AC method of factoring polynomials is easier with polynomials that have values of A and C with many possible factorizations. But if either A or C is prime or if both are prime, for example, the other method is easier I think.