Answer: Dividing (x⁴ - 5x² + 2x - 8) by (x + 2) using polynomial long division:
x³ - 2x² - x + 4
________________________
x + 2 | x⁴ - 5x² + 2x - 8
| x⁴ + 2x³
| _____________
-2x³ + 2x²
-2x³ - 4x²
_____________
6x² + 2x
6x² + 12x
_____________
-10x - 8
Therefore, the quotient is x³ - 2x² - x + 4 and the remainder is -10x - 8.
Explanation: