In Response To 'Re: Re: Polynomial factorization by roots?'
As a side note, I tried this out on my HP-50g.
When I entered X^4+2*X^2+1 and pressed "FACTOR" I got the answer (X+i)^2*(X-i)^2
pressing "COLLECT" for the same polynomial I got the answer (X^2 + 1)^2
I tried it on the polynomial X^3-3*X^2-2*X+6
FACTOR -> (X-3)*(X+SQRT)*(X-SQRT)
COLLECT -> (X-3)*(X^2-2)
The HP-50g also beats the pants off of Mathematica in unit management.