**Solution:**

To find the value of *a*, we need to check if *x-a* is a factor of the polynomial *x^3 - ax^2 + 2x - a - 1*.

Let's use synthetic division to test if *x-a* is a factor.

1. **Synthetic Division**

Synthetic division is a simplified method of dividing polynomials. We will divide the given polynomial by *x-a* using synthetic division.

**Step 1:** Set up the synthetic division table.

| | | | | |
|---|---|---|---|---|
| a | 0 | -a | 2 | -a-1 |

**Step 2:** Bring down the first coefficient, which is *1*.

| | | | | |
|---|---|---|---|---|
| a | 1 | -a | 2 | -a-1 |

**Step 3:** Multiply *a* (the divisor) by the value we brought down, which is *1*. Write the result below the next coefficient.

| | | | | |
|---|---|---|---|---|
| a | 1 | -a | 2 | -a-1 |
| | | | | |
| | | | | |

| | | | | |
|---|---|---|---|---|
| a | 1 | -a | 2 | -a-1 |
| | | | | a |
| | | | | |

**Step 4:** Add the result of the multiplication to the next coefficient.

| | | | | |
|---|---|---|---|---|
| a | 1 | -a | 2 | -a-1 |
| | | | | a |
| | | | | |

| | | | | |
|---|---|---|---|---|
| a | 1 | -a | 2 | -a-1 |
| | | | | a |
| | | | | |

**Step 5:** Repeat steps 3 and 4 until we reach the last coefficient.

| | | | | |
|---|---|---|---|---|
| a | 1 | -a | 2 | -a-1 |
| | | | | a |
| | | | | a |
| | | | | |

| | | | | |
|---|---|---|---|---|
| a | 1 | -a | 2 | -a-1 |
| | | | | a |
| | | | |