Find the other factor I got this answer, and was told it is partially wrong. Should I break it down further? 

Two factors have a product of $3\times9^{2x}-6\times27^x$. One of the factors is $3^x-2$. What is the other factor?

Here is what I did: $$3\times9^{2x}-6\times27^x=3\times9^x\times9^x-6\times3^x\times9^x=3\times9^x(9^x-2\times3^x)=3\times9^x\times3^x(3^x-2)$$
So the other factor is $=3\times27^x$

As Robert said in a comment, your answer is indeed mathematically correct. Any way in which it is "partially wrong" is almost surely due to some preference of the person checking your solution.
