Question

What is the quotient when (10n^2-37n-12) is divided by (n-4)?

Answer 1

I used synthetic division to determine the quotient.  Dividing by n-4 in long div. is equivalent to div. by 4 in synth. div.:

   __________________

4 /   10       -37         -12

                  40          12

 -----------------------------------

     10          3            0

Since there's no remainder, the quotient is 10x+3, which is obtained using the coefficients shown at the bottom above.