Solution:
To find the remainder using the remainder theorem, we divide the polynomial (2x³ + 5x² + x - 2) by (2x + 7):

Using polynomial long division:
```
2x^2 - 3x + 16
_______________________
2x + 7 | 2x^3 + 5x^2 + x - 2
- (2x^3 + 7x^2)
_______________
- 2x^2 + x
- (- 2x^2 - 7x)
_______________
8x - 2
- (8x + 28)
_______________
- 30

Therefore, the remainder of the division (2x³ + 5x² + x - 2) ÷ (2x + 7) is -30.