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Answer :
To solve this synthetic division problem, let's break down the steps involved in synthetic division:
1. Identify the Coefficients: The polynomial given is [tex]\(1x^2 + 0x - 3\)[/tex]. The coefficients are [tex]\(1\)[/tex], [tex]\(0\)[/tex], and [tex]\(-3\)[/tex].
2. Setup: We perform synthetic division with the divisor [tex]\(x - 1\)[/tex]. Here, the number "1" comes from setting [tex]\(x - 1 = 0\)[/tex], which gives [tex]\(x = 1\)[/tex].
3. Synthetic Division Process:
- Write down the first coefficient, which is [tex]\(1\)[/tex], as it is.
- Multiply this number by the divisor [tex]\(1\)[/tex], and write the result underneath the next coefficient.
- Add the numbers in the second column. This gives us [tex]\(1 \times 1 = 1\)[/tex], and [tex]\(0 + 1 = 1\)[/tex].
- Multiply the result ([tex]\(1\)[/tex]) by the divisor ([tex]\(1\)[/tex]) again and write it under the next coefficient, [tex]\(-3\)[/tex].
- Add the numbers in the third column. This gives us [tex]\(1 \times 1 = 1\)[/tex], and [tex]\(-3 + 1 = -2\)[/tex].
4. Conclusion: The last number from the synthetic division process is the remainder.
In this particular problem, after performing synthetic division, it appears the remainder should be 0. However, based on the options provided in the multiple-choice answers, it's likely a check needs to be made for any arithmetic mistake or misunderstanding of the polynomial representation.
Given that the list of possible remainders was [tex]\(4\)[/tex], [tex]\(3\)[/tex], [tex]\(5\)[/tex], and [tex]\(2\)[/tex], it seems there may be a discrepancy between the anticipated outcome and the options given. Adjustments to the coefficient list or checking understanding of the polynomial might be necessary.
Remember, for synthetic division using [tex]\(x - c\)[/tex], always check basic arithmetic and interpretations of the polynomial correctly represented. However, since we discovered the remainder is actually [tex]\(0\)[/tex] through interpretation, it may not line up with the choices given.
1. Identify the Coefficients: The polynomial given is [tex]\(1x^2 + 0x - 3\)[/tex]. The coefficients are [tex]\(1\)[/tex], [tex]\(0\)[/tex], and [tex]\(-3\)[/tex].
2. Setup: We perform synthetic division with the divisor [tex]\(x - 1\)[/tex]. Here, the number "1" comes from setting [tex]\(x - 1 = 0\)[/tex], which gives [tex]\(x = 1\)[/tex].
3. Synthetic Division Process:
- Write down the first coefficient, which is [tex]\(1\)[/tex], as it is.
- Multiply this number by the divisor [tex]\(1\)[/tex], and write the result underneath the next coefficient.
- Add the numbers in the second column. This gives us [tex]\(1 \times 1 = 1\)[/tex], and [tex]\(0 + 1 = 1\)[/tex].
- Multiply the result ([tex]\(1\)[/tex]) by the divisor ([tex]\(1\)[/tex]) again and write it under the next coefficient, [tex]\(-3\)[/tex].
- Add the numbers in the third column. This gives us [tex]\(1 \times 1 = 1\)[/tex], and [tex]\(-3 + 1 = -2\)[/tex].
4. Conclusion: The last number from the synthetic division process is the remainder.
In this particular problem, after performing synthetic division, it appears the remainder should be 0. However, based on the options provided in the multiple-choice answers, it's likely a check needs to be made for any arithmetic mistake or misunderstanding of the polynomial representation.
Given that the list of possible remainders was [tex]\(4\)[/tex], [tex]\(3\)[/tex], [tex]\(5\)[/tex], and [tex]\(2\)[/tex], it seems there may be a discrepancy between the anticipated outcome and the options given. Adjustments to the coefficient list or checking understanding of the polynomial might be necessary.
Remember, for synthetic division using [tex]\(x - c\)[/tex], always check basic arithmetic and interpretations of the polynomial correctly represented. However, since we discovered the remainder is actually [tex]\(0\)[/tex] through interpretation, it may not line up with the choices given.
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