1) The quotient should be (3n^2 + 9n + 5)

You didn't divide by 2

2) I don't know either, but from what I see, n^2 + 4n + 4 is a perfect square (ie you get 144 which is a square number when n = 1)

Which suggests that they tried in (-2) and found that it worked for the polynomial once more after factoring out (x+2)