This is a great place and time to apply synthetic division. Since you are dividing the 3rd order poly by (a+2), let the divisor in synth. div. be -2.
Then:
_________________
-2 / 1 6 12 8
_____-2_-8 -8____________
1 4 4 0
Since there is no remainder, -2 is a root and (x+2) is a factor of the poly.
The quotient comes from those coefficinets 1 4 4
and is 1a^2 + 4a + 4, whose factors are (a+2)^2.
