Trinomial Factoring – nice site and last detail
September 28, 2007 am30 6:09 am
So I wrote about why we should factor, some background skills (and banning FOIL), factoring by grouping, and breaking the middle. That’s really it, except for a few details, and the wrap up.
- History. I learned breaking the middle from Steve Conrad at an Association of Mathematics Teachers of New York State event five years ago. I’m guessing it was the Fall conference in Syracuse, but I might have the year wrong.
- Most people hunt for factors of Π. Instead, we use numbers that add to Σ. Much simpler: if the product is too large, spread the numbers out, if it is too small, move them together. If you miss the target when passing up or down one number, your expression is non-factorable
- For negative Σ, look for numbers with that difference.
- And here is a wonderful demo of breaking the middle from a private Wisconsin Resource center (can be purchased for off-line use – ignore the FOIL part): Wisconsin Demo.
Click that demo a bunch of times.
JD2718 
“breaking the middle”, eh? good terminology!
i usually call it “the split method”, which i learned
online somewhere, probably during the brief fuss
over this slight variant (silly story here)
a few years ago. the text that i first learned it from
(about ten years ago; unless i spaced it out, my algebra
classes in the early seventies presented only “trial and error”
[which, of course, the nomenklatura would now prefer
that we call “guess and check” …]) called it the “AC” method.
the text we *currently* use (at the same campus where
i learned “AC”) calls it “by grouping” (which i object to
since that already means something else …). i’ll probably
be breaking a lot of middles from now on …