Explanation:
Let's perform polynomial long division to find the quotient:
```
_______________________
x + 5 | 4x^2 + 14x - 9
4x^2 + 20x
-------------
-6x - 9
-6x - 30
--------
21
```
The quotient is:
```
4x + 6 - (6x + 9)/(x + 5)
```
Therefore, the correct option for the quotient is:
4x + 6 - 6x - 9
which simplifies to:
-2x - 3