One thing you should learn to do, and this is very, very important: Check your potential answers by expanding them to see if you end up with your original problem. Have you learned the FOIL method? You must have learned how to expand them before getting into factoring.
For example, with that, let's check your last attempt:
Oops, not yet correct. Can you tell what you did wrong from the result? That last term was from multiplying the last part of each factor (the 11^2) together. What would need to be multiplied to make 11^2 rather than 11^4?
That is not factoring - thats solving - you need (x+??)(x-??) - don't give up, just try again!
Have a read of this Difference of two squares - Wikipedia, the free encyclopedia