ehh, in real life, I use about 15% of what I learned in HS and about 25% of what I learned in college. I wouldn't worry about knowing vs. not. Plus, if you can do too much, employers don't like that either.
As for your question, most of the times you can graph it to find the zeros (when x = 0), you can use on of those answers to factor. However, if there are imaginary numbers (trying to solve the square root of a negative number) then it won't pick up those. I may be forgetting much as I haven't used non-practical math in 5 years.