Answer :
To find the remainder when dividing the polynomial by the divisor using synthetic division, follow these steps:
1. Identify the Coefficients and the Root:
- The polynomial is represented by the coefficients `4`, `6`, and `-2`.
- Since we are dividing by [tex]\(x - 1\)[/tex], the root we use for synthetic division is `1`.
2. Set Up Synthetic Division:
- Write the root (`1`) on the left side.
- Write the coefficients `4`, `6`, `-2` in a row.
3. Perform Synthetic Division:
- Bring down the leading coefficient `4` below the line.
- Multiply this `4` by the root (`1`), giving `4`, and place this value under the next coefficient (`6`).
- Add `6` and `4` to get `10`. Write `10` below the line.
- Multiply `10` by the root (`1`), giving `10`, and place it under the next coefficient (`-2`).
- Add `-2` and `10` to get `8`. Write `8` below the line.
4. Read the Results:
- The numbers below the line represent the new coefficients of the quotient polynomial.
- The last number written under the line, `8`, is the remainder.
Therefore, the remainder of the synthetic division is `8`.
So the correct answer is:
B. 8
1. Identify the Coefficients and the Root:
- The polynomial is represented by the coefficients `4`, `6`, and `-2`.
- Since we are dividing by [tex]\(x - 1\)[/tex], the root we use for synthetic division is `1`.
2. Set Up Synthetic Division:
- Write the root (`1`) on the left side.
- Write the coefficients `4`, `6`, `-2` in a row.
3. Perform Synthetic Division:
- Bring down the leading coefficient `4` below the line.
- Multiply this `4` by the root (`1`), giving `4`, and place this value under the next coefficient (`6`).
- Add `6` and `4` to get `10`. Write `10` below the line.
- Multiply `10` by the root (`1`), giving `10`, and place it under the next coefficient (`-2`).
- Add `-2` and `10` to get `8`. Write `8` below the line.
4. Read the Results:
- The numbers below the line represent the new coefficients of the quotient polynomial.
- The last number written under the line, `8`, is the remainder.
Therefore, the remainder of the synthetic division is `8`.
So the correct answer is:
B. 8
