## Swing it, Baby!

Here is a way to factor trinomials that I’d never seen before. It came my way via the tutoring center. I’m working on a proof, but it seems really convincing. Check it out. It is a lot easier than the reverse foil or AC-methods. Does anyone know who came up with it?

This entry was posted on Wednesday, October 16th, 2013 at 10:26 pm and is filed under Algebra, teaching.
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The technique seems to be just a confusing way of multiplying by the coefficient of x^2 so that you get a perfect square coefficient. Factorising as per normal with that and then dividing that coefficient back out again at the end. Using the example in the video:

y = 2 x^2 – 13 x – 45

2y = 4 x^2 – 26 x – 90 = (2x)^2 – 13 (2x) – 90

2y = ((2x) – 18)((2x) + 5)

y = (x – 18)(2x + 5)

Where I have (2x) in the above the video just writes x… It would be clearer (and less dodgy) if a temporary variable w=2x was introduced. I’m not a big fan of this method.

By the way, the underlying trick seems to be similar to James Tanton’s prefered way of completing the square.

Oops…. typo in the last line of the maths above!

I definitely know what you mean. It bothers me too that the expression is not kept equivalent all the way through. But after having so many students struggle with the mechanics of factoring, I’m ready to make a deal with the devil for 10 or 20% more getting through. I haven’t actually used it in class yet, so I can’t vouch that it is any easier for students than the AC method. It does seem promising though. I might test drive it next semester.