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Answer :
Sure! Let's go through the synthetic division step-by-step to find the remainder.
We have a polynomial with coefficients 1, -3, and 2. We are using a divisor of 2 for the synthetic division.
Here's how we perform the synthetic division:
1. Setup: Write down the coefficients of the polynomial: 1, -3, 2. Write the divisor (2) to the left.
2. Bring down the first coefficient: Start by bringing down the first coefficient, which is 1.
3. Multiply and Add:
- Multiply the number you brought down (1) by the divisor (2): [tex]\(1 \times 2 = 2\)[/tex].
- Add this result to the next coefficient: [tex]\(-3 + 2 = -1\)[/tex].
4. Repeat the process:
- Multiply the result from the addition (-1) by the divisor (2): [tex]\(-1 \times 2 = -2\)[/tex].
- Add this to the last coefficient: [tex]\(2 + (-2) = 0\)[/tex].
5. Identify the remainder: The last number after performing the addition is the remainder.
Therefore, the remainder of the synthetic division is 0.
In this problem, the calculated remainder is 0, but that's not one of the options given in the list. It appears there might be a mistake in the options provided, as none of them match the correct remainder.
We have a polynomial with coefficients 1, -3, and 2. We are using a divisor of 2 for the synthetic division.
Here's how we perform the synthetic division:
1. Setup: Write down the coefficients of the polynomial: 1, -3, 2. Write the divisor (2) to the left.
2. Bring down the first coefficient: Start by bringing down the first coefficient, which is 1.
3. Multiply and Add:
- Multiply the number you brought down (1) by the divisor (2): [tex]\(1 \times 2 = 2\)[/tex].
- Add this result to the next coefficient: [tex]\(-3 + 2 = -1\)[/tex].
4. Repeat the process:
- Multiply the result from the addition (-1) by the divisor (2): [tex]\(-1 \times 2 = -2\)[/tex].
- Add this to the last coefficient: [tex]\(2 + (-2) = 0\)[/tex].
5. Identify the remainder: The last number after performing the addition is the remainder.
Therefore, the remainder of the synthetic division is 0.
In this problem, the calculated remainder is 0, but that's not one of the options given in the list. It appears there might be a mistake in the options provided, as none of them match the correct remainder.
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