lost a Mathematica 7.0 that had gone 2.5 days on
Factor[x^3-3^(3/5)+2^(1/5), Extension -> {5^(1/3),2^(1/5),3^(1/5)}]
its linear factor should be
x - (3^(1/5) + 4^(1/5) - 54^(1/5) + 72^(1/5))/5^(2/3)
and of course the quadratic cofactor is irreducible.
mike