Step by step synthetic division, what is the quotient: (2x3 – 2x – 12) ÷ (x – 2) ?

( 2 x³ - 2 x - 12 ) : ( x - 2 ) 

   2   · /  2     0     - 2    - 12
          /         4       8       12
       
             2     4       6        0
    We will multiply 2, 4 and 6 by 2 and add them to the number in the next column.
    Finally:
  q ( x ) = 2 x²  +  4 x + 6