Step-by-step explanation:
x⁴ + 4x³ - 5x² + x - 3 ÷ x² + x - 3 = x² + 3x - 5
- x⁴ + x³ - 3x²
-------------------------
0 3x³ - 2x² + x - 3
- 3x³ + 3x² - 9x
-------------------------------
0 - 5x² + 10x - 3
- - 5x² - 5x + 15
-------------------------------------
0 15x - 18
the result is therefore
x² + 3x - 5 + (15x - 18)/(x² + x - 3)
