Have you seen this method? I ran across it several years ago (I think in a Mathematics Teacher magazine). I loooove it - it's less work than grouping and less guessing than guess & check. We call it the "ac" method. http://www.scribd.com/doc/82987376/A1-9-4b-notesThese are some of my class notes, so if you have any questions about what I did, please let me know! :)Kristen
I have seen method 3 called slide and divide. Because you slide a over (when you multiply by c) and then you divide by a at the end. I have had the most success teaching my students this method.
One ofmy fellow teachers uses this method and she calls it the bottoms up method because in the end you bring the bottom to the top. And the kids usually start singing the song as they go!
The final method works because of the rational root theorem!