Question

find the quotient x^3+5x^2+5/(x+2)

Answer 1

Use synth. div., with divisor -2:

      -----------------------
-2  /   1   5   0    5
              -2   6   -12
     ------------------------
         1    -3   6     -7

The quotient is x^2 - 3x + 6 with a remainer of   -7 / (x+2).