List the "General Strategy" for factoring a polynomial? I think there are only 3 steps.?

Answer 1

Factoring a general polynomial can be a very
daunting task. Often one factors it modulo
many small primes and then uses a version
of the Chinese remainder theorem to
construct a factorisation over the integers.
There is an algorithm by Berlekamp that
is useful in this regard.
See D. Knuth, Art of Computer Programming,
Vol. 2, Chapter 4 for complete details.