For the polynomial 2x^3 - 3x^2 + 2x - 13, the coefficients are 2, -3, 2, -13. Write them in a single row. Place the test root 3 to the left and in its own box.
If you perform the synthetic division, you'll get what you see in the attached image.
The final answer is
Note: the quotient is 2x^2+3x+11; the remainder is 20. The remainder is found by the last item in the bottom row. The coefficients of the quotient are the remaining other values in the bottom row.