Answer :
To find the remainder when using synthetic division, we'll follow a simple process using the values from the problem.
For synthetic division:
1. Understand the Setup:
- The divisor is represented by the number in front of the vertical bar, which is [tex]\(1\)[/tex].
- The coefficients of the polynomial are given as 2, -3, and 2.
2. Perform Synthetic Division:
- Step 1: Bring down the first coefficient. So, we start with 2.
- Step 2: Multiply the divisor (1) by the result (2) and add it to the next coefficient (-3):
[tex]\[
1 \times 2 = 2; \quad 2 + (-3) = -1
\][/tex]
- Step 3: Multiply the divisor (1) by the result (-1) and add it to the next coefficient (2):
[tex]\[
1 \times -1 = -1; \quad -1 + 2 = 1
\][/tex]
3. Identify the Remainder:
- After performing the steps, the last number in our row, 1, is the remainder.
Therefore, the remainder of the division is [tex]\(\boxed{1}\)[/tex].
For synthetic division:
1. Understand the Setup:
- The divisor is represented by the number in front of the vertical bar, which is [tex]\(1\)[/tex].
- The coefficients of the polynomial are given as 2, -3, and 2.
2. Perform Synthetic Division:
- Step 1: Bring down the first coefficient. So, we start with 2.
- Step 2: Multiply the divisor (1) by the result (2) and add it to the next coefficient (-3):
[tex]\[
1 \times 2 = 2; \quad 2 + (-3) = -1
\][/tex]
- Step 3: Multiply the divisor (1) by the result (-1) and add it to the next coefficient (2):
[tex]\[
1 \times -1 = -1; \quad -1 + 2 = 1
\][/tex]
3. Identify the Remainder:
- After performing the steps, the last number in our row, 1, is the remainder.
Therefore, the remainder of the division is [tex]\(\boxed{1}\)[/tex].
