How do I solve this using long division?

Answer:
You can't.
Step-by-step explanation:
When you divide it you get x+5.
Answer:
(x - 2)(x + 5)
Step-by-step explanation:
x +5
----------------------
x - 2 | x² + 3x - 10
x² - 2x ↓
------------------------
5x - 10
5x - 10
------------------------
0 ← remainder = 0
quotient = x + 5
Then x² + 3x - 10 = (x - 2)(x + 5 )