Simplifying Polynomials

Q: The two polynomials

[Graphics:inoutbgr2.gif][Graphics:inoutbgr48.gif]

are equivalent:

[Graphics:inoutbgr2.gif][Graphics:inoutbgr49.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr50.gif]

How can I convert a polynomial like [Graphics:inoutbgr51.gif] to [Graphics:inoutbgr52.gif]?

Daniel Lichtblau (danl@wolfram.com) answers: [Graphics:inoutbgr53.gif] and [Graphics:inoutbgr54.gif] give the same result when applied to [Graphics:inoutbgr55.gif].

[Graphics:inoutbgr2.gif][Graphics:inoutbgr56.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr57.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr58.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr59.gif]

To get the factorized coefficients, you can use either the three-argument form of [Graphics:inoutbgr60.gif],

[Graphics:inoutbgr2.gif][Graphics:inoutbgr61.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr62.gif]

or [Graphics:inoutbgr63.gif] followed by [Graphics:inoutbgr64.gif].

[Graphics:inoutbgr2.gif][Graphics:inoutbgr65.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr66.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr67.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr68.gif]