Divide using synthetic division x^2+15x+52 by x+9

To divide the polynomial x^2 + 15x + 52 by x + 9 using synthetic division, we set up the division table as follows:

-9 | 1 15 52
-9 -54
-----------------
1 6 -2

The quotient is x + 6 and the remainder is -2. Therefore, the result of dividing x^2 + 15x + 52 by x + 9 is (x + 6) with a remainder of -2.