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The wikipedia example of Polynomial Long Division starts with:

Divide the first term of the numerator by the highest term of the denominator

if the denominator is $x-3$, and we don't know $x$, how to know which is highest? $x$ or $3$?

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    "Highest term" means highest degree term. Polynomial long division is analogous to long division of integers in radix representation.2011-02-10
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    Also: the $x$ in a polynomial does not represent an unknown number.2011-02-10
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    Arturo: But in fact $\rm\:x\:$ does represent an "unknown number". More precisely it represents a universal (generic) $\rm\:R$-algebra element. $\rm\ R[x]$ is defined so that the equations true in it are precisely those ring-theoretic equations that hold true in every $\rm\ R$-algebra. Therefore an equation is true in $\rm\:R[x]\:$ iff it is a universal identity of $\rm\:R$-algebras. For example see my post [here](http://bit.ly/h7Q81Y) and [see here](http://bit.ly/hUZWoP) and [see here](http://bit.ly/hynx03).2011-02-10
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    Maybe we could improve the wikipedia article on Polynomial Long Division then? I wonder if others have been similarly confused.2011-03-31
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    @David Kohler: +1 great idea. I did little bit, but it can still be improved.2011-04-01

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"highest" here means not "greatest", but the one with the highest power of $x$ (which in this case is $x$).

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    that is, the "highest-degree" term2011-04-10