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Answer :
To find the remainder using synthetic division, follow these steps:
1. Identify the Coefficients: We start with the coefficients of the polynomial, which are 4, 6, and -1, corresponding to the terms [tex]\(4x^2 + 6x - 1\)[/tex].
2. Choose the Divisor: The divisor is given as 1.
3. Perform Synthetic Division:
- Step 1: Bring down the leading coefficient (4) as the starting remainder.
- Step 2: Multiply the remainder (initially 4) by the divisor (1), which gives 4. Add this product to the next coefficient (6). This calculation is: [tex]\(4 \times 1 + 6 = 10\)[/tex].
- Step 3: Now multiply the new result (10) by the divisor (1), getting 10. Add this to the next coefficient (-1). This is: [tex]\(10 \times 1 - 1 = 9\)[/tex].
4. Determine the Remainder: By the end of the process, the final calculated value, which is 9, is the remainder.
So, the remainder of this synthetic division problem is 9.
The correct answer is B. 9.
1. Identify the Coefficients: We start with the coefficients of the polynomial, which are 4, 6, and -1, corresponding to the terms [tex]\(4x^2 + 6x - 1\)[/tex].
2. Choose the Divisor: The divisor is given as 1.
3. Perform Synthetic Division:
- Step 1: Bring down the leading coefficient (4) as the starting remainder.
- Step 2: Multiply the remainder (initially 4) by the divisor (1), which gives 4. Add this product to the next coefficient (6). This calculation is: [tex]\(4 \times 1 + 6 = 10\)[/tex].
- Step 3: Now multiply the new result (10) by the divisor (1), getting 10. Add this to the next coefficient (-1). This is: [tex]\(10 \times 1 - 1 = 9\)[/tex].
4. Determine the Remainder: By the end of the process, the final calculated value, which is 9, is the remainder.
So, the remainder of this synthetic division problem is 9.
The correct answer is B. 9.
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