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In our test suite (comprising qqbar etc.) something like 10% of all inputs to fmpz_poly_factor have a cyclotomic factor. We should investigate whether trial division by cyclotomic polynomials can be done quickly enough (e.g. mod 2^63 and with precomputed tables) to be worth it.
Other small linear and quadratic factors are also reasonably common, but perhaps not common enough for trial division.