TxO Math Bowl 2024 - Team Contest - Problem 9

The function 6x^{12} + 3x^3 + 2 is divided by x + 2, producing a quotient and a remainder. The quotient is then divided by x + 2 again to produce another quotient and remainder. This process is repeated until the new quotient is a constant. Compute the absolute value of the sum of all the remainders that appear during this process.