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Answer :
To solve the synthetic division problem and find the remainder, let's go through the process step-by-step:
We are dividing the polynomial [tex]\(x^3 + 0x^2 - 3x + 2\)[/tex] by [tex]\(x - 1\)[/tex].
1. Identify the coefficients: The coefficients of the polynomial [tex]\(x^3 + 0x^2 - 3x + 2\)[/tex] are [tex]\([1, 0, -3, 2]\)[/tex].
2. Identify the divisor root: The divisor is [tex]\(x - 1\)[/tex], which means the root (value of [tex]\(x\)[/tex] that makes the divisor zero) is [tex]\(1\)[/tex].
3. Perform synthetic division:
- Bring down the first coefficient: [tex]\(1\)[/tex].
- Multiply this by the root (1) and add to the next coefficient:
- [tex]\(1 \times 1 = 1\)[/tex], then [tex]\(0 + 1 = 1\)[/tex].
- Multiply the result by the root (1) and add to the next coefficient:
- [tex]\(1 \times 1 = 1\)[/tex], then [tex]\(-3 + 1 = -2\)[/tex].
- Multiply the result by the root (1) and add to the next coefficient:
- [tex]\(-2 \times 1 = -2\)[/tex], then [tex]\(2 - 2 = 0\)[/tex].
4. Determine the remainder: The last number at the bottom is the remainder.
In this case, after performing synthetic division, the remainder is [tex]\(0\)[/tex].
Therefore, the correct answer is:
None of the options (2, 4, or 5) are correct, since the remainder is actually 0. It seems there might be an error in the choices provided.
We are dividing the polynomial [tex]\(x^3 + 0x^2 - 3x + 2\)[/tex] by [tex]\(x - 1\)[/tex].
1. Identify the coefficients: The coefficients of the polynomial [tex]\(x^3 + 0x^2 - 3x + 2\)[/tex] are [tex]\([1, 0, -3, 2]\)[/tex].
2. Identify the divisor root: The divisor is [tex]\(x - 1\)[/tex], which means the root (value of [tex]\(x\)[/tex] that makes the divisor zero) is [tex]\(1\)[/tex].
3. Perform synthetic division:
- Bring down the first coefficient: [tex]\(1\)[/tex].
- Multiply this by the root (1) and add to the next coefficient:
- [tex]\(1 \times 1 = 1\)[/tex], then [tex]\(0 + 1 = 1\)[/tex].
- Multiply the result by the root (1) and add to the next coefficient:
- [tex]\(1 \times 1 = 1\)[/tex], then [tex]\(-3 + 1 = -2\)[/tex].
- Multiply the result by the root (1) and add to the next coefficient:
- [tex]\(-2 \times 1 = -2\)[/tex], then [tex]\(2 - 2 = 0\)[/tex].
4. Determine the remainder: The last number at the bottom is the remainder.
In this case, after performing synthetic division, the remainder is [tex]\(0\)[/tex].
Therefore, the correct answer is:
None of the options (2, 4, or 5) are correct, since the remainder is actually 0. It seems there might be an error in the choices provided.
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