[krackers]

I don't see how this statement is useful, because if an alg is "tractable" iff it is poly-time then n^10 algorithms would be considered "tractable". I think the real reason we care about P in a CS-theoretic sense is because it's a closed group under various operations, which allows us to talk about things in an implementation-oblivious fashion.

In practice in the real world we care only about low-degree P though (usually n < 3 at most), are really interested in linear & nlogn, and care about constant factors.

There's also Quasi-Polynomial time algorithms which are interesting because they straddle the line between P and EXPTIME.