help, i'm stuck in algebra and i can't get out!

The following is an email sent to my sister, who I have already called four times this morning, once at 4:30 am her time (sorry Becky!!) It's not my fault she lives in Colorado and happens to be a math tutor. She walked us through the following equations a couple of times, and she did such a good job that we thought we 'had' it! (When I say 'we' I mean Tawny and I). But we still didn't get the right answer, I think our answers are pretty good, but I guess they have to be all the way right...
By the way the funky Os are supposed to be square root symbols, I guess people don't blog enough about math to need those...

"Step by step:
Please give the standard form of a function with rational coefficients and the given zeros
Zeros: Ö3, 1-Ö5
What we’ve been doing-
(xÖ3)(x+Ö3) (x-(1-Ö5)) (x+(1-Ö5))
x2+x-xÖ5-x+xÖ5-1+5 x2+4
X2 +xÖ3-xÖ3-3 x2-3

we’re pretty much screwed up and desperately need your help!

we also don’t know what to do on the : 2, 2-i"

Now you may be wondering why I'm so into algebra all of a sudden. Tawny has finals this week and two algebra tests, one today. I had her skip school and told her we'd work on these problems until she felt confident enough to take the test. We did get all but 4 done, and that took us from 7:30 am to 5:30 pm, with a 1 1/2 hour break in there where I took a nap with Enoch and Danni.
So if anyone can help with these, or the Binomial Theorem, you would be my hero!