## Saturday, February 4, 2012

### Polynomial Division?

I'm trying to put together lesson plans for my Algebra 2 students' unit on polynomials and rational expressions.  The curriculum we're using doesn't have any lessons on factoring polynomials beyond quadratics, but our state standards do require factoring higher order polynomials.  I'm kind of torn as to how to teach this because I can't think of very many compelling reasons students would want to factor higher order polynomials without spending a lot more time on this topic than I want to.  I feel like it's a pretty useful skill for students to have- I know at least my calculus student has encountered polynomial division a few times this year, but I just feel a little tepid on the topic.  I don't know how important the broader math world regards this topic.  Is it worth spending more than a day on in Algebra 2?  Is there any way to make it fun and or applicable?  I've been searching around and I can't find anything at all that other teachers have put together other than drill and kill worksheets.  Anyway, here are two worksheets I've thrown together to help students factor higher order polynomials.  I think they should provide two relatively straight forward lessons albeit a little boring.  I would love any advice on spicing this topic up, or maybe compelling reasons to either go more in depth into the topic or to drop it all together.

Factoring With Pascal's Triangle Polynomial Division Exploratory Ws

One other note: Maybe this is something novices do, but I am a little torn about font choice.  I know in the larger scheme of things font matters so little, but I've heard so many people making comments about Comic Sans MS being unprofessional yet my students love it.  My first year teaching I was just playing with fonts, switching back and forth and not really caring, but my algebra 1 students who have had terrible experiences with math latched onto the assignments I printed up in Comic Sans as being friendlier and easier to understand.  They said it made math less scary.  Since then I've been using exclusively Comic Sans.  Another educator told me to stop using it because it was unprofessional, but when I polled all my students, they insisted that I stick to Comic Sans font.  Notice I did decide to switch fonts for the second worksheet.  I tried to find something that was equally friendly but didn't have the same stigma.  Sadly it's tiny.  What a silly thing to obsess over yet shouldn't I listen to my students?

1. From your worksheets it doesn't look like students have been working with polynomials geometrically. I like the geometric/box/table method both because multiple representations supports greater understanding and because topics like completing the square and polynomial division can become one-day lessons. These aren't topics easily discarded from the curriculum but not ones you want to spend weeks on.

I know it's not easy interpreting a presentation from slides alone, but to get an idea of what I mean by a geometric representation of polynomials, you can check out a presentation I made last fall at an NCTM Regional Conference. I swear someday I'm going to flesh the whole thing out in a series of blog posts, but it's been rather hard to find the time.

I've found some other resources that should help:

Riley's "Polydoku" post: http://larkolicio.us/blog/?p=95

Polynomial factoring video: http://www.youtube.com/watch?v=Fwq9P_aBzl4 (The explanation in the video isn't the best when considered by itself -- there was probably a lot of work in class to get to this point -- but it will show you some of the mechanics of the factoring.)

If you're intrigued but these examples aren't making much sense, let me know and maybe we can work out a way for me to demonstrate and ask questions via Google+ Hangout or Skype.

2. Wow! Thank you so much. I'll check out all these resources. I do introduce multiplying binomials and factoring quadratics geometrically, but I wasn't sure how to apply it to the mechanics of polynomials division. I'm so excited to find other resources out there because I feel like I've been googling polynomial division for an age without finding anything useful.