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 th

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 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_preview.pdf#page=23 https://minireference.com/static/excerpts/noBSmath_v5_previe...