Answer:
Here are the steps to divide 4x^3 + 2x^2 + 3x + 4 by x + 4 using long division:
```
4x^2 - 14x + 59
________________________
x + 4 | 4x^3 + 2x^2 + 3x + 4
- (4x^3 + 16x^2)
---------------------
-14x^2 + 3x
-(-14x^2) - 56x
----------------
59x + 4
59x + 236
--------
-232
```
Therefore, the quotient is 4x^2 - 14x + 59, and the remainder is -232.