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What is the remainder in the synthetic division problem below?

[tex]
1 \overline{1} \quad 2 \quad -3 \quad 2
[/tex]

A. 2
B. 3
C. 4
D. 5

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].

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