• When you are figuring out a term of the quotient, you can always match the first term of the dividend (as long as the degree of the divisor is less than or equal to the degree of the dividend). This may require fractions, however. For example:
  

          (-3/2)x   + (-11/2)
          _________________________
  2x - 2 /     3x^2 - 5x + 5
              -3x^2 + 6x
              ---------
                    -11x + 5
                    -11x + 11
                    ---------
                          -6
  

• Fill in for terms that are missing. In your problem there is no "x" term. So I filled in for it with "0x".
• After you multiply and subtract, you bring down the next term, not the next digit.

         8x^2 + (-4x) +   12
        __________________________
2x + 6 /16x^3 + 40x^2 +    0x + 72
        16x^3 + 48x^2
        -------------
                -8x^2 +    0x
                -8x^2 + (-24x)
                --------------
                          24x + 72
                          24x + 72
                          --------
                                 0