I mentioned the "airplane" method for factoring in a recent post. Someone asked me what that was, so I thought I'd share. I have seen a lot of methods for factoring a quadratic with a leading coefficient. Out of the ones I've tried, this is my favorite. The analogy to an airplane is a bit of a stretch, but students seem to remember it pretty well. So I'll take it. I should also mention that, before I show this to students, I always spend some time letting them work on these by trial and error. I figure a process like this is worthless if they don't actually understand what they are doing. Once I feel like students understand the concept but they are still struggling to get every problem to work, I show them this. We treat it like a shortcut, and boy do they appreciate it! Here is an example: First, my students know they will need two binomials, so I start with two sets of parenthesis. Then I put the leading coefficient in each parenthesis. Hopefully, the students have a problem with this. We talk about why it is a problem, and I promise them that we will get rid of the extra 2 before we're all done. Then, multiply a and c. (See the airplane wings? Use your imagination.) Look for two numbers with product ac and sum b. (Propeller? I know this is really a stretch.) Put those numbers in the parenthesis. Divide the extra 2. (The landing? Maybe.) It is pretty cheesy, but when students are having trouble I can say something like "you forgot the landing", and they know what I mean. Done. For something like this, you may need to divide both binomials. I point out how dividing by 3 and by 2 is the same as dividing by 6. We just choose the division that will keep integers. Happy factoring!