Answer :
To solve this synthetic division problem, we're going to divide the polynomial represented by the coefficients `[4, 6, -1]` by the number `1`. Let's go through the synthetic division process step-by-step:
1. Setup:
- Write down the coefficients of the polynomial: 4, 6, and -1.
- The divisor is 1. This is the number we will use to perform synthetic division.
2. Process:
- Start by bringing down the first coefficient, which is 4.
- Multiply this number (4) by the divisor (1) and write the result under the next coefficient.
- Add this result to the next coefficient (6): [tex]\( 4 \times 1 = 4 \)[/tex], then [tex]\( 4 + 6 = 10 \)[/tex].
- Write 10 below to replace the second coefficient.
- Multiply the new number (10) by the divisor (1) and write down the result under the next coefficient.
- Add this result to the last coefficient (-1): [tex]\( 10 \times 1 = 10 \)[/tex], then [tex]\( 10 + (-1) = 9 \)[/tex].
3. Conclusion:
- The remainder produced by the synthetic division process is 9.
Therefore, the remainder of the division is 9, which means the correct answer is:
A. 9
1. Setup:
- Write down the coefficients of the polynomial: 4, 6, and -1.
- The divisor is 1. This is the number we will use to perform synthetic division.
2. Process:
- Start by bringing down the first coefficient, which is 4.
- Multiply this number (4) by the divisor (1) and write the result under the next coefficient.
- Add this result to the next coefficient (6): [tex]\( 4 \times 1 = 4 \)[/tex], then [tex]\( 4 + 6 = 10 \)[/tex].
- Write 10 below to replace the second coefficient.
- Multiply the new number (10) by the divisor (1) and write down the result under the next coefficient.
- Add this result to the last coefficient (-1): [tex]\( 10 \times 1 = 10 \)[/tex], then [tex]\( 10 + (-1) = 9 \)[/tex].
3. Conclusion:
- The remainder produced by the synthetic division process is 9.
Therefore, the remainder of the division is 9, which means the correct answer is:
A. 9
