In Response To 'Re: Re: Polynomial factorization by roots?'
I haven't played with it much, so I really can't say. Check the documentation under the "Factor" command. It seems you have to know what term you want in the factor, in this case "i". The example given uses it to get Sqrt to show up in the factorization.
"Factor" assumes that all coefficients in the factors are rational numbers. with "Extension" you can extend the types of factors it will produce. (You can use the "Roots" function to find the factor you're looking for.)