This post is a little personal venting along with some serious math. I am in an Algebra 2 training today, and the instructor is doing some long division for finding slant asymptotes. Okay, nothing wrong with that, but I ask why we aren’t using synthetic division when we just finished using synthetic division in the previous example when the WHOLE room (minus 2 pp) yells it me, “Because it can’t be done.” When I insist it can work, they challenge me to put it on the board, they just don’t believe it. The session ends before I can.

The frustrating thing is, the entire room of math teachers with the exception of 2 others are completely and totally wrong. At least 2 other people had my back.

As evidence, see this paper by

Okay, I admit, that paper is kind of rough reading. How about some easier stuff then.

From Pat’s blog, we have the following articles: Link 1, Link 2, Link 3, and Link 4.

And, just to prove to myself that Pat is correct, (and he is, don’t doubt it) I tried a problem side by side with the long division I know works:

Really, it works. I especially like the fact that synthetic division does not always need a 1 in front of the leading term.

Oops, I just did another synthetic division that is impossible!

I think I need to do four more so that I can be like the White Queen and do six impossible things before breakfast.

And yes, I am getting to the training tomorrow early so these can be on the board when everyone walks in. Don’t tell me something is impossible unless it truly is. Calling something impossible because you don’t want to think or learn about it is kind of like saying the quadratic equation y = x^{2} – x + 7 has no solutions. It has solutions, they just aren’t nice and easy like you are used to.

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Special thanks to Pat, who introduced me to this in 2009 in his blog.

[…] I read Glenn’s post Never Tell Me It Can’t Be Done. Again, we get so fixated on the process we’ve been ‘taught’ or even used to […]

Thank you for this post. I can’t say that I’ve ever questioned when you can or can’t use synthetic division so I really appreciate seeing what is possible.

Glen, I herd it was impossible for years before I sat down and derived this approach. In math, “it’s impossible!” requires the same standard of proof as ” it’s possible.”

By the way, I have a little on history of terms from stats, z, t, etc on a page at http://pballew.net/etyindex.html and a couple of stats relate blogs you might enjoy. http://pballew.blogspot.com/2011/09/standard-deviation-as-distance.html for example.. just search stats… thanks for an interesting blog

Thank you Pat. I will dive into the history of z, t etc today.

[…] never say never to a kid, they’ll prove you wrong! Math teachers will too – see Never tell me it can’t be done.) They were still struggling – so I was trying to think of a new method. Then the […]