Final answer:
To divide using synthetic division, we write the polynomial in descending order of powers, change the sign of the divisor and set it equal to zero, perform synthetic division, and find the quotient and remainder.
Step-by-step explanation:
To divide using synthetic division, we first write the polynomial in descending order of powers. So the polynomial becomes 6x³ - 4x + 13. Next, we change the sign of the divisor and set it equal to zero, so x + 2 = 0. Solving for x, we find x = -2. Now, we apply synthetic division by placing the coefficients of the polynomial in a division table, and divide by -2:
-2 │ 6 -4 13
│ -12 32
──────
6 -16 45
The result of the division is 6x² - 16x + 45. Therefore, the quotient is 6x² - 16x + 45 and there is a remainder of 0.