Factoring trinomials whose leading coefficient (a) is 1. Notes included.
I do not teach the "guess and check" method of factoring; students struggle with it because there is no process. The "AC method" uses a process/algorithm to easily factor a trinomial; it relies on the concept of factoring by grouping.
1. Multiply a and c
2. Find factors of "ac" that add up to "b"
3. Rewrite "bx" using the factors you found
4. Factor by grouping
Because of this method, the only "new" thing between this lesson and the previous one does not seem as daunting as it would by using guess and check - the students need only find the factors that add up to b and rewrite bx using those factors. Then, they factor by grouping, and will usually pick up pretty quickly that that step is like the previous lesson.
Once they know the general process, factoring is simple, especially when a > 1 (Lesson 6).
I also show the students a chart (in example #6) that is helpful in determining the signs, it really becomes "fool proof". When the signs need to be different, I tell the students that "the larger factor takes the sign of the middle term" and make sure to use that phrase repeatedly. It really takes all the "guessing" - and thus the anxiety - out of factoring.