Answer:To apply synthetic division for the polynomial using the root , follow these steps:1. Setup: Write down the coefficients of the polynomial:.2. Synthetic Division Process:Write on the left and the coefficients in a row.Bring down the leading coefficient .Multiply by and write the result under the next coefficient:.Add this result to the next coefficient:.Repeat this process for the remaining coefficients.Here’s how it looks:2 | 1 -2 -3 -9 10 | 2 0 -6 -12------------------------- 1 0 -3 -15 -23. Result: The bottom row represents the coefficients of the quotient polynomial and the remainder: with a remainder of .Therefore, the result of the synthetic division is:You can further analyze or factor the quotient polynomial if needed.