Answer :

To find the remainder in the synthetic division problem, we need to divide the polynomial [tex]\(4x^2 + 6x - 3\)[/tex] by [tex]\(x - 1\)[/tex] using synthetic division. Here's how to do it step-by-step:

1. Setup Synthetic Division:
- Write down the coefficients of the polynomial: [tex]\(4, 6, -3\)[/tex].
- Since we are dividing by [tex]\(x - 1\)[/tex], use [tex]\(1\)[/tex] as the divisor.

2. Perform Synthetic Division:
- Bring down the first coefficient, 4. This will be the start of the first row.
- Multiply this result by the divisor (1) and write the answer below the line, under the second coefficient (6).
- Add the number just written to the second coefficient (6), and write the result below the line.
- Repeat this process: take the last result, multiply by the divisor, and add to the next coefficient.

Here's what it looks like in steps:

```
Coefficients: 4 6 -3
↓
____
1 | 4 6 -3
| 4
|------------
4 10
| → 10 x 1 = 10
|------------
4 10 7
```

3. Read the Result:
- The last number obtained, 7, is the remainder.

Therefore, the remainder when the polynomial [tex]\(4x^2 + 6x - 3\)[/tex] is divided by [tex]\(x - 1\)[/tex] is 7.

Looking at the provided options, the correct choice is:

D. 7

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Rewritten by : Barada