Answer :
To find the remainder in the given synthetic division problem, we follow these steps:
1. Identify the Polynomial and Divisor: We are given the coefficients [tex]\([1, 2, -3]\)[/tex], which correspond to the polynomial [tex]\(x^2 + 2x - 3\)[/tex].
2. Set Up for Synthetic Division: We are dividing by [tex]\(x - 1\)[/tex], which means the divisor term is 1. This is because synthetic division uses the root of the divisor when setting up the calculation.
3. Perform the Synthetic Division:
- Write the first coefficient [tex]\(1\)[/tex] in the result row.
- Multiply this result by the divisor term (1) and add the next coefficient (2):
- [tex]\(1 \times 1 + 2 = 3\)[/tex]. Write [tex]\(3\)[/tex] in the result row.
- Repeat this process: Multiply the last result [tex]\(3\)[/tex] by the divisor term (1) and add the last coefficient (-3):
- [tex]\(3 \times 1 - 3 = 0\)[/tex]. Write [tex]\(0\)[/tex] in the result row.
4. Interpret the Result: The sequence of numbers in the result, [tex]\([1, 3, 0]\)[/tex], gives us the quotient and the remainder. The remainder of the division is the last number in the sequence, which is [tex]\(0\)[/tex].
Therefore, the remainder of the synthetic division is [tex]\(0\)[/tex].
1. Identify the Polynomial and Divisor: We are given the coefficients [tex]\([1, 2, -3]\)[/tex], which correspond to the polynomial [tex]\(x^2 + 2x - 3\)[/tex].
2. Set Up for Synthetic Division: We are dividing by [tex]\(x - 1\)[/tex], which means the divisor term is 1. This is because synthetic division uses the root of the divisor when setting up the calculation.
3. Perform the Synthetic Division:
- Write the first coefficient [tex]\(1\)[/tex] in the result row.
- Multiply this result by the divisor term (1) and add the next coefficient (2):
- [tex]\(1 \times 1 + 2 = 3\)[/tex]. Write [tex]\(3\)[/tex] in the result row.
- Repeat this process: Multiply the last result [tex]\(3\)[/tex] by the divisor term (1) and add the last coefficient (-3):
- [tex]\(3 \times 1 - 3 = 0\)[/tex]. Write [tex]\(0\)[/tex] in the result row.
4. Interpret the Result: The sequence of numbers in the result, [tex]\([1, 3, 0]\)[/tex], gives us the quotient and the remainder. The remainder of the division is the last number in the sequence, which is [tex]\(0\)[/tex].
Therefore, the remainder of the synthetic division is [tex]\(0\)[/tex].
