This worksheet provides practice for synthetic division, guiding students through interpreting results and solving polynomial division problems.

1. The dividend is $x^3 + 2x^2 - x - 2$.
2. The quotient is $3x^3 - 10x^2 + 8x + 27$.
3. The dividend is $(x + 2)(x^3 + x + 3)$.
4. The completed synthetic division is:
```
2 | 2 1 3 10
| 4 10 26
-------------------
2 5 13 36
```
5. The completed synthetic division is:
```
3 | 1 -4 1 2
| 3 -3 -6
-----------------
1 -1 -2 -4
```
6. $(2x^3 + 4x^2 - 3x - 6) \div (x + 3)$
```
-3 | 2 4 -3 -6
| -6 6 -9
------------------
2 -2 3 -15
```
The quotient is $2x^2 - 2x + 3$ with a remainder of $-15$. So, the answer is $2x^2 - 2x + 3 - \frac{15}{x + 3}$.
7. $(x^3 - 6x^2 + 9) \div (x - 4)$
```
4 | 1 -6 0 9
| 4 -8 -32
------------------
1 -2 -8 -23
```
The quotient is $x^2 - 2x - 8$ with a remainder of $-23$. So, the answer is $x^2 - 2x - 8 - \frac{23}{x - 4}$.
8. $(4x^3 + 27x^2 + 3x + 64) \div (x + 7)$
```
-7 | 4 27 3 64
| -28 7 -70
-------------------
4 -1 10 -6
```
The quotient is $4x^2 - x + 10$ with a remainder of $-6$. So, the answer is $4x^2 - x + 10 - \frac{6}{x + 7}$.
9. $(x^4 - 16x^2 - 40x - 25) \div (x - 5)$
```
5 | 1 0 -16 -40 -25
| 5 25 45 25
--------------------------
1 5 9 5 0
```
The quotient is $x^3 + 5x^2 + 9x + 5$ with no remainder. So, the answer is $x^3 + 5x^2 + 9x + 5$.