Using synthetic division, what is the quotient (3x3 + 4x − 32) ÷ (x − 2)?

The question is set up in the following way:

2] 3   0   4   -32



Here the 2 is from when x-2 is set equal to zero and then solved for x, the rest is from the the number being divided with zero taking the place of the x^2.

Then the following happens:

2] 3   0   4   -32   
         6  12   32

    3   6  16   0

Here the following happens: 
1. We drop down the first coefficient, which is 3
2. We take this coefficient and multiply it by the two in the corner and get 6.
3. We place this six under the second coefficient (0) and add them together and get 6.
4. We take this 6 and multiply it by the two in the corner and get 12.
5. We take this 12 and put it under the third coefficient (4), add them together and get 16.
6. We take the 16 and multiply it by the two in the corner and get 32.
7. We take the 32 and place in under the forth coefficient and get zero.

This gives us the coefficients of the final answer in the order 3, 6 and 16 with no remaninders which gives us 3x^2+6x+16.