Sorry for the image-ness, but I can't do exponents in forum code, I'm pretty sure.
Anyway, I don't need help as much with the problem (although of course that would be nice) as much as the concept. I read the chapter of my textbook and relevant Wikipedia articles, but I still don't really understand how you solve based on the zero that's given.
According to my answer key, the correct answer is (highlight) C) { 2, 7, -1/3 }
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I got help from one of my friends, so I guess never mind.
For anyone who might be interested, the answer is that if you know 2 is a zero then (x-2) is a factor, and then you can divide the polynomial by (x-2) and come up with a second-degree polynomial which should be factorable - the end result is (x-2)(x-7)(3x+3)=0
and as a note synthetic division does fine here.
