Answer :
To find the remainder when performing synthetic division, follow these steps:
1. First, identify the coefficients of the polynomial. In this case, the coefficients are 4, 6, and -1 from the sequence [tex]\(4,\ 6,\ -1\)[/tex].
2. The divisor used in synthetic division is derived from the factor [tex]\(x - \text{divisor}\)[/tex], and in this problem, the divisor is given as 1. This means you are dividing the polynomial by [tex]\(x - 1\)[/tex].
3. Start the synthetic division process by bringing down the first coefficient, 4.
4. Multiply the divisor (1) by the number you just brought down (4) and write the result (4) underneath the second coefficient (6).
5. Add the result (4) to the second coefficient (6) to get 10.
6. Multiply the divisor (1) by this result (10) and write it under the third coefficient (-1).
7. Add this result (10) to the third coefficient (-1) to get 9.
8. The final value obtained after the addition is 9, which is the remainder of the synthetic division.
So, the remainder in this synthetic division problem is 9. Therefore, the correct answer is B. 9.
1. First, identify the coefficients of the polynomial. In this case, the coefficients are 4, 6, and -1 from the sequence [tex]\(4,\ 6,\ -1\)[/tex].
2. The divisor used in synthetic division is derived from the factor [tex]\(x - \text{divisor}\)[/tex], and in this problem, the divisor is given as 1. This means you are dividing the polynomial by [tex]\(x - 1\)[/tex].
3. Start the synthetic division process by bringing down the first coefficient, 4.
4. Multiply the divisor (1) by the number you just brought down (4) and write the result (4) underneath the second coefficient (6).
5. Add the result (4) to the second coefficient (6) to get 10.
6. Multiply the divisor (1) by this result (10) and write it under the third coefficient (-1).
7. Add this result (10) to the third coefficient (-1) to get 9.
8. The final value obtained after the addition is 9, which is the remainder of the synthetic division.
So, the remainder in this synthetic division problem is 9. Therefore, the correct answer is B. 9.
