Answer :
Sure, let's go through the synthetic division process to find the remainder.
We're given the synthetic division row [tex]\(1: 1, 2, -3, 3\)[/tex]. In synthetic division, this typically represents the coefficients of a polynomial divided by a linear factor of the form [tex]\(x - c\)[/tex].
### Step-by-step Solution:
1. Write down the coefficients:
- Our polynomial coefficients are [tex]\(1, 2, -3,\)[/tex] and [tex]\(3\)[/tex].
2. Perform synthetic division:
- We assume the divisor is [tex]\(x - c\)[/tex]. The remainder in synthetic division is usually the last number after completing the division process.
3. Understand the result:
- Since synthetic division results in a row, the last number in this row represents the remainder.
4. Conclusion:
- The last coefficient provided here is [tex]\(3\)[/tex], which suggests that the remainder of the division is 3.
Therefore, the remainder in the synthetic division problem is [tex]\(\boxed{3}\)[/tex].
We're given the synthetic division row [tex]\(1: 1, 2, -3, 3\)[/tex]. In synthetic division, this typically represents the coefficients of a polynomial divided by a linear factor of the form [tex]\(x - c\)[/tex].
### Step-by-step Solution:
1. Write down the coefficients:
- Our polynomial coefficients are [tex]\(1, 2, -3,\)[/tex] and [tex]\(3\)[/tex].
2. Perform synthetic division:
- We assume the divisor is [tex]\(x - c\)[/tex]. The remainder in synthetic division is usually the last number after completing the division process.
3. Understand the result:
- Since synthetic division results in a row, the last number in this row represents the remainder.
4. Conclusion:
- The last coefficient provided here is [tex]\(3\)[/tex], which suggests that the remainder of the division is 3.
Therefore, the remainder in the synthetic division problem is [tex]\(\boxed{3}\)[/tex].
