Answer :
To find the remainder when performing synthetic division, we first need to understand the process using the given numbers.
Let's break it down step by step:
1. Identify the Coefficients: From the problem, the coefficients of the polynomial are [tex]\(1\)[/tex], [tex]\(2\)[/tex], and [tex]\(-3\)[/tex].
2. Identify the Divisor: The number [tex]\(1\)[/tex] given at the start of the synthetic division indicates the value we are dividing by, which is also the root.
3. Setting Up Synthetic Division:
- Write the divisor, which is [tex]\(1\)[/tex], to the left.
- Write the coefficients [tex]\(1\)[/tex], [tex]\(2\)[/tex], and [tex]\(-3\)[/tex] in a row to the right.
4. Process of Synthetic Division:
- Bring down the first coefficient, [tex]\(1\)[/tex], directly below the line.
- Multiply this number ([tex]\(1\)[/tex]) by the divisor ([tex]\(1\)[/tex]) and write the result under the next coefficient ([tex]\(2\)[/tex]).
- Add this result to the next coefficient: [tex]\(2 + 1 = 3\)[/tex].
- Multiply [tex]\(3\)[/tex] (the result from the previous step) by the divisor ([tex]\(1\)[/tex]) and write the result under the next coefficient ([tex]\(-3\)[/tex]).
- Add this result to the next coefficient: [tex]\(-3 + 3 = 0\)[/tex].
5. Conclusion:
- The remainder is the final value you have after summing up under the last coefficient, which is [tex]\(0\)[/tex].
The remainder of the synthetic division process is [tex]\(0\)[/tex], which means the correct answer is not provided among the options. It appears there might be an error in the given problem or the options.
However, based on the described solution, if any more context or correction is needed, I would be glad to assist further!
Let's break it down step by step:
1. Identify the Coefficients: From the problem, the coefficients of the polynomial are [tex]\(1\)[/tex], [tex]\(2\)[/tex], and [tex]\(-3\)[/tex].
2. Identify the Divisor: The number [tex]\(1\)[/tex] given at the start of the synthetic division indicates the value we are dividing by, which is also the root.
3. Setting Up Synthetic Division:
- Write the divisor, which is [tex]\(1\)[/tex], to the left.
- Write the coefficients [tex]\(1\)[/tex], [tex]\(2\)[/tex], and [tex]\(-3\)[/tex] in a row to the right.
4. Process of Synthetic Division:
- Bring down the first coefficient, [tex]\(1\)[/tex], directly below the line.
- Multiply this number ([tex]\(1\)[/tex]) by the divisor ([tex]\(1\)[/tex]) and write the result under the next coefficient ([tex]\(2\)[/tex]).
- Add this result to the next coefficient: [tex]\(2 + 1 = 3\)[/tex].
- Multiply [tex]\(3\)[/tex] (the result from the previous step) by the divisor ([tex]\(1\)[/tex]) and write the result under the next coefficient ([tex]\(-3\)[/tex]).
- Add this result to the next coefficient: [tex]\(-3 + 3 = 0\)[/tex].
5. Conclusion:
- The remainder is the final value you have after summing up under the last coefficient, which is [tex]\(0\)[/tex].
The remainder of the synthetic division process is [tex]\(0\)[/tex], which means the correct answer is not provided among the options. It appears there might be an error in the given problem or the options.
However, based on the described solution, if any more context or correction is needed, I would be glad to assist further!
