To find the area of the garden that belongs to Pablo, we need to subtract Golden's area from the total area of the garden.
- Total area of the garden: \( 5x^2 - 3x + 10 \)
- Area belonging to Golden: \( 2x^2 + 4x - 2 \)
Now, we subtract Golden's area from the total area:
\[ \text{Area belonging to Pablo} = \text{Total area} - \text{Area belonging to Golden} \]
Thus, we can write:
\[ \text{Area belonging to Pablo} = (5x^2 - 3x + 10) - (2x^2 + 4x - 2) \]
Now, we distribute the negative sign through Golden's expression:
\[ = 5x^2 - 3x + 10 - 2x^2 - 4x + 2 \]
Next, we combine like terms:
- Combine \(5x^2\) and \(-2x^2\):
\[ 5x^2 - 2x^2 = 3x^2 \]
- Combine \(-3x\) and \(-4x\):
\[ -3x - 4x = -7x \]
- Combine \(10\) and \(2\):
\[ 10 + 2 = 12 \]
Putting it all together, we have:
\[ \text{Area belonging to Pablo} = 3x^2 - 7x + 12 \]
Thus, the area of the garden that belongs to Pablo is:
\[ \boxed{3x^2 - 7x + 12} \text{ square feet} \]