## Dividing (a^2 - 28) by (a - 5)

This problem involves dividing a polynomial by a binomial. We can use **long division** to solve it. Here's how:

### Step 1: Set up the Long Division

```
a + 5
a - 5 | a^2 + 0a - 28
```

- We write the dividend (a^2 - 28) inside the division symbol. Notice that we've added a 0a term as a placeholder for the missing linear term.
- The divisor (a - 5) is written outside the division symbol.

### Step 2: Divide the Leading Terms

- 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 division symbol, aligned with the a^2 term.

```
a + 5
a - 5 | a^2 + 0a - 28
a^2 - 5a
```

### Step 3: Multiply and Subtract

- Multiply the divisor (a - 5) by the term we just wrote above (a). This gives us
**a^2 - 5a**. - Write this result below the dividend.
- Subtract the two polynomials:

```
a + 5
a - 5 | a^2 + 0a - 28
a^2 - 5a
-------
5a - 28
```

### Step 4: Bring Down the Next Term

- Bring down the next term from the dividend (-28).

```
a + 5
a - 5 | a^2 + 0a - 28
a^2 - 5a
-------
5a - 28
```

### Step 5: Repeat Steps 2-4

- Divide the leading term of the new polynomial (5a) by the leading term of the divisor (a). This gives us
**5**. - Write
**5**above the division symbol, aligned with the constant term. - Multiply the divisor (a - 5) by 5. This gives us
**5a - 25**. - Subtract the two polynomials:

```
a + 5
a - 5 | a^2 + 0a - 28
a^2 - 5a
-------
5a - 28
5a - 25
-------
-3
```

### Step 6: Remainder

- We're left with a remainder of
**-3**.

### The Result

Therefore, (a^2 - 28) divided by (a - 5) is **a + 5 with a remainder of -3**. We can express this as:

**(a^2 - 28) / (a - 5) = a + 5 - 3/(a - 5)**