Answer: 3x + 6 - 3/(x+6)
Explanation:
You can use synthetic division to solve this problem. Use the picture I attached as a reference.
The number on the left comes from solving x + 6 = 0. x = -6.
You then set up a half-rectangle type of shape and put each coefficient from the term with the highest power to the lowest power on the top. The coefficients are 3, 24, and 33 (if the polynomial skips a power, for example, 3x^2 and then 33 then you would put 0 in place of 0x^1).
First, drop the leading coefficient down and write it under the half-box shape. Then, multiply the -6 by whatever you just dropped, and write it in the position that is up and to the right. So 3 times -6 is -18 which I wrote up and to the right of 3. Then you would add together the number on top of that, so 24 + (-18) is 6. Do the same process. 6 times -6 is -36, and 33 + -36 is -3. -3 is the remainder since there is nothing we can do with it now.
Now, for the final answer, we simply just subtract a power from the original polynomial's leading term (which was 3x^2) and attach the new numbers to it. The new leading term's power is 1, so slap the 3 on there to get 3x. The second term's power is 0, so it's just +6. So far we have 3x + 6. Then, for the remainder, we have to divide the remaining number by the original divisor (which was x+6).
Put these steps together and we get 3x + 6 - 3/(x+6).