>> Because I don't know what polynomial division actually "is" yet.
> 
> Opposite of polynomial multiplication.
> 
> (x^3+3x^2-4x)/(x^2-x) = ???

As I understand it, the product of two polynomials is a formula that 
produces the same result as running the two polynomials and then taking 
the product of their answers. And this product is guaranteed to always 
be a polynomial.

It is not immediately clear to be that the quotient of two polynomials 
is necessarily a polynomial.

>> I didn't say you don't need to know how to do long division - I said 
>> you don't need to spend 3 years practising it for several hours per day.
> 
> It makes things later in life, assuming you go on with studying maths, a 
> lot easier.  At university I used to cringe at the people who used their 
> calculators so often to do what they really should be doing in their 
> head. When you are tackling a large problem it is a huge advantage do be 
> able to do at least the basics very quickly in your head.

Hell, I can't even multiply numbers in my head!

I'm good at understanding principles and elligant mathematical theories. 
I'm not good at memorising vast amounts of unstructured data.

And if you think your experience was bad, imagine being in a room full 
of undergraduates and finding that only 2 of them know what "logarithm" 
means. (Obviously one was me. The other one was that crazy rugby player 
from Manchester. I remember at the time feeling quite guilty for 
assuming he was stupid just because has acted like a complete psychopath 
all day long...)

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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