## Simplifying the Expression (a^2 - 8a - 26) / (a + 2)

This expression represents a rational expression, where the numerator is a quadratic polynomial and the denominator is a linear polynomial. We can simplify this expression by performing polynomial long division.

**1. Setting up the Long Division**

We set up the long division as follows:

```
a - 10
a + 2 | a^2 - 8a - 26
-(a^2 + 2a)
-10a - 26
-(-10a - 20)
-6
```

**2. Performing the Division**

**Step 1:**Divide the leading term of the dividend (a^2) by the leading term of the divisor (a). This gives us 'a'. Write 'a' above the line as the first term of the quotient.**Step 2:**Multiply the divisor (a + 2) by the term 'a' we just found, and write the result (a^2 + 2a) below the dividend.**Step 3:**Subtract the result from the dividend. This leaves us with -10a - 26.**Step 4:**Bring down the next term (-26) to form the new dividend.**Step 5:**Divide the leading term of the new dividend (-10a) by the leading term of the divisor (a). This gives us '-10'. Write '-10' above the line as the next term of the quotient.**Step 6:**Multiply the divisor (a + 2) by the term '-10', and write the result (-10a - 20) below the new dividend.**Step 7:**Subtract the result from the new dividend. This leaves us with -6.

**3. The Result**

The final result of the long division is:

**(a^2 - 8a - 26) / (a + 2) = a - 10 - 6/(a + 2)**

**Important Note:** The remainder of the division is -6, which is written over the original divisor (a + 2). This indicates that the original expression cannot be completely simplified. However, we have successfully expressed the original expression as the sum of a polynomial (a - 10) and a rational expression (-6/(a + 2)).