Answer :
Let's find the remainder of the synthetic division problem using a step-by-step process. We'll assume that the division is performed by the divisor related to the question.
1. Understand the terms:
- Coefficients of the polynomial: 1, 2, -3, and 2.
- The polynomial is thus [tex]\( f(x) = x^3 + 2x^2 - 3x + 2 \)[/tex].
2. Assume the divisor:
- We are typically working with a divisor of the form [tex]\( (x - c) \)[/tex]. For synthetic division, a common choice is [tex]\( x - 1 \)[/tex], which implies [tex]\( c = 1 \)[/tex].
3. Set up for synthetic division:
- The coefficients (1, 2, -3, 2) from the polynomial are written in a row.
- The value we are dividing by (c) is written to the left. Here, c = 1.
4. Perform the synthetic division process:
- Bring down the first coefficient: 1.
- Multiply this number (1) by the divisor (1), placing the result (1) underneath the second coefficient.
- Add the second coefficient (2) and the number underneath it (1), giving a new entry of 3.
- Multiply 3 by the divisor (1) and place the result (3) underneath the next coefficient (-3).
- Add -3 and 3 to get 0.
- Multiply 0 by the divisor (1) and place the result (0) under the final coefficient (2).
- Add 2 and 0 to get 2.
5. Identifying the remainder:
- The last number obtained after addition (2) is the remainder.
Therefore, the remainder when dividing [tex]\( x^3 + 2x^2 - 3x + 2 \)[/tex] by [tex]\( x - 1 \)[/tex] is 2.
So the answer is:
B. 2
1. Understand the terms:
- Coefficients of the polynomial: 1, 2, -3, and 2.
- The polynomial is thus [tex]\( f(x) = x^3 + 2x^2 - 3x + 2 \)[/tex].
2. Assume the divisor:
- We are typically working with a divisor of the form [tex]\( (x - c) \)[/tex]. For synthetic division, a common choice is [tex]\( x - 1 \)[/tex], which implies [tex]\( c = 1 \)[/tex].
3. Set up for synthetic division:
- The coefficients (1, 2, -3, 2) from the polynomial are written in a row.
- The value we are dividing by (c) is written to the left. Here, c = 1.
4. Perform the synthetic division process:
- Bring down the first coefficient: 1.
- Multiply this number (1) by the divisor (1), placing the result (1) underneath the second coefficient.
- Add the second coefficient (2) and the number underneath it (1), giving a new entry of 3.
- Multiply 3 by the divisor (1) and place the result (3) underneath the next coefficient (-3).
- Add -3 and 3 to get 0.
- Multiply 0 by the divisor (1) and place the result (0) under the final coefficient (2).
- Add 2 and 0 to get 2.
5. Identifying the remainder:
- The last number obtained after addition (2) is the remainder.
Therefore, the remainder when dividing [tex]\( x^3 + 2x^2 - 3x + 2 \)[/tex] by [tex]\( x - 1 \)[/tex] is 2.
So the answer is:
B. 2
