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

Nope, same as dividing two integers doesn't always give an integer answer, 
you sometimes end up with fractional parts in the answer.

eg 10/4 = 2 + 2/4

same as

(x^3+2x^2)/(x^2+1) = x+2 + (-x-2)/(x^2+1)

> 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.

Didn't your course require a maths A level for entry?

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