## How-To: Synthetic Division

During my Algebra 2 unit on polynomials, I had asked my (support) class if they would like to stick to just using polynomial long division, which works for every single problem, or if they would like to also learn another method (synthetic) that, while far quicker, only works in certain situations.  It was almost unanimous that they favored sticking to polynomial long division, which was fairly surprising to me. I almost figured they would want a quicker method, but their rationale was sound.  They thought that having another method would just trip them up, and they didn’t really see a point if it could only be used for linear binomials.

However, a few weeks after our unit on polynomials, we had a bit of down time so I introduced synthetic just for fun.  The students caught on quickly, but still preferred long division since it made more sense to them. (I agree that Synthetic is harder to wrap one’s head around.  It feels a bit more “magic.”)  Unfortunately, most of the class was gone that day due to an optional viewing of the school play being offered for students during the first four periods of the day.

As we start moving toward reviewing for finals, I figured I’d make a slideshow for students to view on their phones if they wanted to get a refresher on synthetic division.  Here it is!  I like it because it has a quiz-yourself and work-at-your-own-pace feel to it.

Do you cover both synthetic and long division for polynomials?  Which does your class seem to prefer?

### 2 thoughts on “How-To: Synthetic Division”

1. Scott Leverentz (@scottmlev) August 2, 2017 / 9:46 pm

Nice reference for students! I soured on synthetic division after reading “Nix the Tricks” despite it not necessarily being a trick. I think in the sense of my students, it was a mindless procedures. I’ve been thoroughly sold since then on using area models and “the box method” for all polynomial multiplication and division. It’s my go to.

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• Math by the Mountain August 18, 2017 / 5:05 am

I’m not much a fan of synthetic division other than for quickly verifying an answer, when it actually is applicable. Otherwise, you’re completely right, it’s a magic trick that makes little sense other than rote procedure.

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