At the risk of providing some information about what is probably going
on,
let me suggest the following.

1. The expand() command in Maxima is almost always the wrong thing to
do if the argument is a polynomial.
ratexpand() or ratsimp() or rat()  will be much faster.  I suspect
that in your timings of Maxima, the major
contributor may be expand.

2. This is not a good test of polynomial factoring, because it does
uses only a trivial part of the algorithm,
and that is the square-free factoring part, that consists of computing
P' a derivative of P and a gcd(P,P').

Mostly you are testing the gcd program, but only the case of the gcd
program for gcd(a,b) where, almost all
the time, a divides b.  So you are not even testing the gcd program,
you are testing polynomial division with remainder.

Now if that is what you want to test, fine.  If you want to test
polynomial factoring, there is a substantial
literature on how to choose polynomials that are difficult to factor.
Especially large degree is not really necessary.

While it is only a speculation on my part, I think what you may also
be timing is the conversion of
relatively large character strings, at least in some cases.

I hope you can straighten this out before you present your results at
your conference.

RJF

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