Question

What is the complete factorization of 108x^2-99y+3

Answer 1

The quadratic formula would "do" this nicely.  a=108; b= -99 and c=3.

Then:
        99 plus or minus sqrt(99^2 - 4(108)(3)
x = -----------------------------------------------------
                              2(108).

Please do the indicated calculations.  You should get 2 roots.  Now, just supposing that x = 2 were a root (it's not one), then the associated factor would be x-2.  Do the same thing with the 2 roots you've just found.