Find the quotient of the rational expression, using Long or Synthetic division 2x^3+5x^2+16x-23 / x-1
Solve using synthetic division:
1 | 2 5 16 -23
+ 0 2 7 23
-----------------
2 7 23 0
The quotient is therefore 2x^2 + 7x + 23
The first number in the top line is 1 because x = 1 (x - 1 is the denominator). The 2, 5, 16, -23 are the coefficents of the numerator. You then use synthetic division to get the coefficients of the quotient and the remainder. You bring the first original coefficient (2) down untouched. You multiply that by the divisor (1) and add to the next coefficient (5). 5 + 2 = 7. You multiply that by the divisor and add to the next coefficient and so on. The last number you get is the remainder.
