Answer :
To solve this problem using synthetic division, we will follow these steps:
1. Identify the divisor: The divisor is (x - 1), as indicated by the number "1" above the line.
2. Set up the coefficients: Write down the coefficients of the polynomial, which are 1, 2, -3, and 3.
3. Perform the synthetic division:
- Bring down the first coefficient (1) as it is.
- Multiply this number by the divisor (1), and write the result under the next coefficient.
- Add this result to the next coefficient (2) to get a new number.
- Continue this process until you have worked through all the coefficients.
So, let's break it down:
1. Initial Coefficients: 1, 2, -3, 3.
2. Steps:
- Bring down the 1.
- Multiply 1 (brought down) by 1 (divisor), which gives 1. Add this to the next coefficient (2), resulting in 3.
- Multiply 3 by 1, which gives 3. Add this to the next coefficient (-3), resulting in 0.
- Multiply 0 by 1, which gives 0. Add this to the last coefficient (3), resulting in 3.
3. Remainder: The final number we obtain after adding is the remainder. In this case, it's 3.
Therefore, the remainder when dividing the polynomial by x - 1 is 3.
The correct answer is D. 3.
1. Identify the divisor: The divisor is (x - 1), as indicated by the number "1" above the line.
2. Set up the coefficients: Write down the coefficients of the polynomial, which are 1, 2, -3, and 3.
3. Perform the synthetic division:
- Bring down the first coefficient (1) as it is.
- Multiply this number by the divisor (1), and write the result under the next coefficient.
- Add this result to the next coefficient (2) to get a new number.
- Continue this process until you have worked through all the coefficients.
So, let's break it down:
1. Initial Coefficients: 1, 2, -3, 3.
2. Steps:
- Bring down the 1.
- Multiply 1 (brought down) by 1 (divisor), which gives 1. Add this to the next coefficient (2), resulting in 3.
- Multiply 3 by 1, which gives 3. Add this to the next coefficient (-3), resulting in 0.
- Multiply 0 by 1, which gives 0. Add this to the last coefficient (3), resulting in 3.
3. Remainder: The final number we obtain after adding is the remainder. In this case, it's 3.
Therefore, the remainder when dividing the polynomial by x - 1 is 3.
The correct answer is D. 3.
