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Answer :
Sure! Let's solve the synthetic division problem step-by-step.
We're given a polynomial with coefficients [4, 6, -3] and we need to perform synthetic division using the divisor (x - 1), which means substituting x = 1 in the division process.
Here's how synthetic division works:
1. Identify the Coefficients: For the polynomial, we have the coefficients 4, 6, and -3. The polynomial is assumed to be in descending order of powers.
2. Perform Synthetic Division:
- Start by bringing down the first coefficient, which is 4.
- Multiply this number by the divisor (which is the value 1, since x - 1 means x = 1) and add it to the next coefficient. So, 4 1 + 6 = 10.
- Repeat this step with the new result. Multiply 10 by the divisor (1) and add it to the next coefficient: 10 1 + (-3) = 7.
3. Identify the Remainder: The last number you obtain in this process is the remainder. In this case, it's 7.
So, the remainder of the synthetic division is 7.
Thus, the correct answer is A. 7.
We're given a polynomial with coefficients [4, 6, -3] and we need to perform synthetic division using the divisor (x - 1), which means substituting x = 1 in the division process.
Here's how synthetic division works:
1. Identify the Coefficients: For the polynomial, we have the coefficients 4, 6, and -3. The polynomial is assumed to be in descending order of powers.
2. Perform Synthetic Division:
- Start by bringing down the first coefficient, which is 4.
- Multiply this number by the divisor (which is the value 1, since x - 1 means x = 1) and add it to the next coefficient. So, 4 1 + 6 = 10.
- Repeat this step with the new result. Multiply 10 by the divisor (1) and add it to the next coefficient: 10 1 + (-3) = 7.
3. Identify the Remainder: The last number you obtain in this process is the remainder. In this case, it's 7.
So, the remainder of the synthetic division is 7.
Thus, the correct answer is A. 7.
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