Divide 3x3+17x2+21x−9

To divide the polynomial \( P(x) = 3x^3 + 17x^2 + 21x - 9 \) by \( x + 3 \) using synthetic division, we can follow these steps:

1. **Identify the zero of the divisor**: For \( x + 3 \), the zero is \( x = -3 \).

2. **Set up the synthetic division**: Write down the coefficients of \( P(x) \), which are \( 3, 17, 21, -9 \).

3. **Carrying out the synthetic division**:

```
-3 | 3 17 21 -9
| -9 -24 9
-----------------------
3 8 -3 0
```

- Bring down the first coefficient (3).
- Multiply -3 by 3 and write it under 17: \( -3 \times 3 = -9 \).
- Add \( 17 + (-9) = 8 \).
- Multiply -3 by 8: \( -3 \times 8 = -24 \), and write it under 21.
- Add \( 21 + (-24) = -3 \).
- Multiply -3 by -3: \( -3 \times -3 = 9 \), and write it under -9.
- Add \( -9 + 9 = 0 \).

4. **Interpret the result**: The bottom row gives the coefficients of the quotient polynomial and the last number (0) is the remainder.

So, we find that the result of the division is:

\[
3x^2 + 8x - 3
\]

Thus, the correct response is:

**3x^2 + 8x - 3**.