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Answer :
Sure! Let's go through the synthetic division process step by step to find the remainder.
We are performing synthetic division for the polynomial represented by the coefficients [tex]\(4, 6, -1\)[/tex] using the divisor [tex]\(x - 1\)[/tex], where 1 is the number you’ll be working with in the synthetic division. The steps are as follows:
1. Write Down the Coefficients: Start by writing the coefficients of the polynomial, which are [tex]\(4, 6, -1\)[/tex].
2. Bring Down the First Coefficient: Bring down the first coefficient, [tex]\(4\)[/tex]. This is the first part of our result.
3. Multiply and Add:
- Multiply the number you brought down (4) by the divisor (1). [tex]\(4 \times 1 = 4\)[/tex].
- Add this result to the next coefficient (6). [tex]\(6 + 4 = 10\)[/tex].
4. Repeat Multiply and Add:
- Now, take the result from the previous addition (10), multiply it by the divisor (1). [tex]\(10 \times 1 = 10\)[/tex].
- Add this result to the next coefficient (-1). [tex]\(-1 + 10 = 9\)[/tex].
5. Result:
- The number [tex]\(9\)[/tex] you get as a result of the last addition is the remainder of the division.
Thus, the remainder of the synthetic division is [tex]\(9\)[/tex].
So, the correct answer is [tex]\(C. 9\)[/tex].
We are performing synthetic division for the polynomial represented by the coefficients [tex]\(4, 6, -1\)[/tex] using the divisor [tex]\(x - 1\)[/tex], where 1 is the number you’ll be working with in the synthetic division. The steps are as follows:
1. Write Down the Coefficients: Start by writing the coefficients of the polynomial, which are [tex]\(4, 6, -1\)[/tex].
2. Bring Down the First Coefficient: Bring down the first coefficient, [tex]\(4\)[/tex]. This is the first part of our result.
3. Multiply and Add:
- Multiply the number you brought down (4) by the divisor (1). [tex]\(4 \times 1 = 4\)[/tex].
- Add this result to the next coefficient (6). [tex]\(6 + 4 = 10\)[/tex].
4. Repeat Multiply and Add:
- Now, take the result from the previous addition (10), multiply it by the divisor (1). [tex]\(10 \times 1 = 10\)[/tex].
- Add this result to the next coefficient (-1). [tex]\(-1 + 10 = 9\)[/tex].
5. Result:
- The number [tex]\(9\)[/tex] you get as a result of the last addition is the remainder of the division.
Thus, the remainder of the synthetic division is [tex]\(9\)[/tex].
So, the correct answer is [tex]\(C. 9\)[/tex].
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