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What is the remainder in the synthetic division problem below?

[tex]\[

\begin{array}{c|cccc}

1 & 1 & 2 & -3 & 3 \\

\end{array}

\][/tex]

A. 4
B. 3
C. 6
D. 5

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].

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