I really like this new way of doing factoring, since 90% of the steps of the explanation are more intuitive and direct than the usual guessing techniques and the complete-the-square technique that leads to the quadratic formula. I was so excited by this new approach that I started rewriting the parts in the math book that explain quadratics, and looking forward to getting rid of the complete-the-square procedure, which many readers find confusing.

However, the Po-Shen Loh method (a.k.a the Viète method) has one big conceptual hurdle at the beginning (the missing 10%), which I had trouble explaining, since it seems to come out of nowhere and not obvious:

> "Two numbers have a sum of 14 exactly when their average is 7."

> "Two numbers have an average is 7 when those numbers are 7-u and 7+u"

via https://www.youtube.com/watch?v=XKBX0r3J-9Y&t=592s

^ both these statements are true and correct, but they seem to come out of nowhere, like one of those "Suppose u = <complicated expression> ..." substitution tricks that are needed to solve certain calculus problems, which are otherwise impossible if you don't know the needed substitution.

The substitution 7-u and 7+u is related to the general idea that any two numbers (or functions) can be written in terms of a symmetric component m (half-sum, or mean) and a half-difference part d:

   given any a, b
   define:
       m = (a+b)/2     (the half-sum of a and b)
       d = (a-b)/2     (half-difference of a and b)
   then:
       a = m + d
       b = m - d

Again, this is totally true (and a very useful math idea that comes up in other places), but not intuitive for beginners.

In the end I decided to stick with the complete-the-square approach: complete-the-square is not that bad, especially when you show the picture: https://minireference.com/static/excerpts/noBSmath_v5_previe...