Allow me to play the devil's advocate for a bit. I think it is useless and a waste of time to teach any factoring other than x^n -y^n = (x-y)*(x^[n-1]+...+y^[n-1]). That gives us geometric sums and many other things. I am a great fan of the difference of squares case, from which we immediately get completing the square (CTS). Since CTS is so much more useful than the quadratic formula (QF), I see no reason to have everyone learn the QF. If these ideas were followed in middle/high school, how much time would be saved? How many fewer students would think math is useless and difficult and not something they want to have anything to do with in their future (and so their carreer options are considerably narrowed)?
JViggs@aol.com wrote: > > try using factoring by re-grouping or grouping.... no guessing... it is in > most precalc and clac books.. i have taught it at the 7th-12 grade levels and > for the most part it works very well.. briefly.... > > 2x^2 - 7x + 6 > > multiply the leding coeficient by the 6 and get +12.. list the factors of > +12... > +3, +4 and -3, -4 > +6, +2 and -6, -2 > +1, +12 and -1, -12 > > then see which ones Combine "add" to -7.. > then break up the middle term > 2x^2 -3x -4x +6 > Factor the 1st two by GCF, then the second two by GCF > x(x-3) -2(2x - 3) > then finish.... (x-2)(2x-3) > Actually you are factoring the (2x - 3) from each.... It works very welll... > all you need is mult/div/add/subtract then GCF factoring.... it is most > difficult as above... when there is a factoring out a negative... and kids > when practicing enough get the two numbers quickly... > > Joseph R. Vignolini > glen cove high school > a.k.a. joe viggs > a.k.a. mr v > a.k.a. Odin > www.mrvignolini.com -- Ladnor Geissinger Math Dept, CB 3250 Phillips Hall Univ of North Carolina Chapel Hill NC 27599, USA