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Decending powers of x

September 26, 2014 4 comments

I was in one of my colleagues lessons this week.and he was teaching the class to expand quadratic brackets. As the lesson went on he noticed that a number of pupils had been writing the X squared term, then the constant term then the X term so he pulled the class together to tell them that conventionally we write quadratic equations in decending powers of x. This is excellent practice and something we all should be encouraging, but it made me think “Why decending powers of x?”

When dealing with quadratic, cubics and quartics up to GCSE and A-Level level we use the convention of decending powers. This is common in all sorts from expanding through long division, even in linear function we use descending powers. However, when we start with series expansions, such as binomial or Taylor’s, we switch to ascending powers. I’m also fairly certain that everything in my second and third year university modules on polynomials was in ascending powers too.

Now don’t get me wrong, I’m happy with the fact we have different conventions here, and I’m not against using them. I’m just inquisitive, and would love to know if there is a reason, and if there is what that reason is. If you do know, I’d love to hear it!

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