Which one of the following sentences is grammatically correct?

1. Since we were behind schedule, we had to work quick.

2. She felt badly that she arrived so late.

3. Of all the students in the class, he asked permission most politely.

4. He sure was real smart to figure that out.

I chose 2 for the answer but I think it could be 3. Thanks for the help. TK
You were tricked, TK.

In (2), 'feel' is a copular verb requiring the adjective 'bad'-- even though many speakers use 'badly' in this structure (Googled: 'feel bad' - 486,000; 'feel badly' -33,400)'

The correct answer is (3).
I guess I was tricked. I thought it was 2. Thanks TK