Answer :
To find the remainder using synthetic division, follow these steps:
1. Identify the coefficients of the polynomial:
The polynomial given has coefficients 1, 2, -3, and 2.
2. Set up the synthetic division:
The divisor is [tex]\(x - 1\)[/tex], which means you will use the value [tex]\(1\)[/tex] for the synthetic division.
3. Begin the synthetic division process:
- Write the leading coefficient (1) below the horizontal line. This is the start of your solution.
- Multiply this number by the value used for division (1 in this case) and write the result under the next coefficient (2).
- Add the result to the next coefficient (2) and write the sum underneath.
4. Continue the process:
- Multiply the result from the previous step with the value for division (1), place it under the next coefficient (-3).
- Add to the coefficient (-3), writing the sum below.
- Do the same steps again for the final coefficient (2).
5. Locate the remainder:
- After completing these steps, the last number you obtain in the row is the remainder.
By following these steps, the remainder you find is 2. Thus, the correct answer is B. 2.
1. Identify the coefficients of the polynomial:
The polynomial given has coefficients 1, 2, -3, and 2.
2. Set up the synthetic division:
The divisor is [tex]\(x - 1\)[/tex], which means you will use the value [tex]\(1\)[/tex] for the synthetic division.
3. Begin the synthetic division process:
- Write the leading coefficient (1) below the horizontal line. This is the start of your solution.
- Multiply this number by the value used for division (1 in this case) and write the result under the next coefficient (2).
- Add the result to the next coefficient (2) and write the sum underneath.
4. Continue the process:
- Multiply the result from the previous step with the value for division (1), place it under the next coefficient (-3).
- Add to the coefficient (-3), writing the sum below.
- Do the same steps again for the final coefficient (2).
5. Locate the remainder:
- After completing these steps, the last number you obtain in the row is the remainder.
By following these steps, the remainder you find is 2. Thus, the correct answer is B. 2.
