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Answer :
Sure! Let's go through the synthetic division process step-by-step to find the remainder when dividing the polynomial [tex]\(4x^2 + 6x - 1\)[/tex] by [tex]\(x - 1\)[/tex].
1. Identify the root:
The divisor is [tex]\(x - 1\)[/tex], and we set [tex]\(x - 1 = 0\)[/tex] to find the root. Therefore, the root is [tex]\(x = 1\)[/tex].
2. Write down the coefficients:
The coefficients of the polynomial [tex]\(4x^2 + 6x - 1\)[/tex] are [tex]\(4, 6,\)[/tex] and [tex]\(-1\)[/tex].
3. Begin the synthetic division process:
- Bring down the first coefficient, which is [tex]\(4\)[/tex].
- Multiply this coefficient by the root (1). So, [tex]\(4 \times 1 = 4\)[/tex].
- Add this result to the next coefficient: [tex]\(6 + 4 = 10\)[/tex].
- Multiply the new result by the root again: [tex]\(10 \times 1 = 10\)[/tex].
- Add this result to the last coefficient: [tex]\(-1 + 10 = 9\)[/tex].
4. Result:
The last number after you finish the synthetic division process is the remainder. In this case, the remainder is [tex]\(9\)[/tex].
Therefore, the remainder when [tex]\(4x^2 + 6x - 1\)[/tex] is divided by [tex]\(x - 1\)[/tex] is [tex]\(\boxed{9}\)[/tex].
1. Identify the root:
The divisor is [tex]\(x - 1\)[/tex], and we set [tex]\(x - 1 = 0\)[/tex] to find the root. Therefore, the root is [tex]\(x = 1\)[/tex].
2. Write down the coefficients:
The coefficients of the polynomial [tex]\(4x^2 + 6x - 1\)[/tex] are [tex]\(4, 6,\)[/tex] and [tex]\(-1\)[/tex].
3. Begin the synthetic division process:
- Bring down the first coefficient, which is [tex]\(4\)[/tex].
- Multiply this coefficient by the root (1). So, [tex]\(4 \times 1 = 4\)[/tex].
- Add this result to the next coefficient: [tex]\(6 + 4 = 10\)[/tex].
- Multiply the new result by the root again: [tex]\(10 \times 1 = 10\)[/tex].
- Add this result to the last coefficient: [tex]\(-1 + 10 = 9\)[/tex].
4. Result:
The last number after you finish the synthetic division process is the remainder. In this case, the remainder is [tex]\(9\)[/tex].
Therefore, the remainder when [tex]\(4x^2 + 6x - 1\)[/tex] is divided by [tex]\(x - 1\)[/tex] is [tex]\(\boxed{9}\)[/tex].
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