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Answer :
Sure! Let's solve the synthetic division problem step by step.
We are given the polynomial represented by the coefficients [tex]\(4\)[/tex], [tex]\(6\)[/tex], and [tex]\(-1\)[/tex]. We need to divide this by [tex]\((x - 1)\)[/tex], since our divisor is [tex]\(1\)[/tex].
Synthetic division is a simpler way to divide a polynomial by a binomial of the form [tex]\(x - c\)[/tex].
Here is how the process goes:
1. Set Up the Problem:
- Write down the coefficients: [tex]\(4, 6, -1\)[/tex].
2. Synthetic Division Steps:
- Bring down the first coefficient [tex]\(4\)[/tex] as is.
- Multiply this number [tex]\(4\)[/tex] by the divisor [tex]\(1\)[/tex] (since we divide by [tex]\(x - 1\)[/tex], [tex]\(c = 1\)[/tex]), which gives us [tex]\(4\)[/tex].
- Add this product to the next coefficient: [tex]\(6 + 4 = 10\)[/tex].
- Multiply the result [tex]\(10\)[/tex] by the divisor [tex]\(1\)[/tex]: [tex]\(10 \times 1 = 10\)[/tex].
- Add this result to the next coefficient: [tex]\(-1 + 10 = 9\)[/tex].
3. Conclusion:
- The last result we get after adding is the remainder of the division.
The remainder is thus [tex]\(9\)[/tex].
So, the correct answer is B. 9.
We are given the polynomial represented by the coefficients [tex]\(4\)[/tex], [tex]\(6\)[/tex], and [tex]\(-1\)[/tex]. We need to divide this by [tex]\((x - 1)\)[/tex], since our divisor is [tex]\(1\)[/tex].
Synthetic division is a simpler way to divide a polynomial by a binomial of the form [tex]\(x - c\)[/tex].
Here is how the process goes:
1. Set Up the Problem:
- Write down the coefficients: [tex]\(4, 6, -1\)[/tex].
2. Synthetic Division Steps:
- Bring down the first coefficient [tex]\(4\)[/tex] as is.
- Multiply this number [tex]\(4\)[/tex] by the divisor [tex]\(1\)[/tex] (since we divide by [tex]\(x - 1\)[/tex], [tex]\(c = 1\)[/tex]), which gives us [tex]\(4\)[/tex].
- Add this product to the next coefficient: [tex]\(6 + 4 = 10\)[/tex].
- Multiply the result [tex]\(10\)[/tex] by the divisor [tex]\(1\)[/tex]: [tex]\(10 \times 1 = 10\)[/tex].
- Add this result to the next coefficient: [tex]\(-1 + 10 = 9\)[/tex].
3. Conclusion:
- The last result we get after adding is the remainder of the division.
The remainder is thus [tex]\(9\)[/tex].
So, the correct answer is B. 9.
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