To find the expression that models the remainder of Alex's workshop space after renting out part of it to Matt, we need to subtract the area rented to Matt from the total area of Alex's workshop.
The expressions given are:
- Alex's workshop area: \( 4x^2 + 7x - 3 \)
- Matt's rented area: \( 2x^2 + 7x - 5 \)
Now, we calculate the remainder by subtracting Matt's area from Alex's area:
\[ (4x^2 + 7x - 3) - (2x^2 + 7x - 5) \]
Distributing the negative sign:
\[ 4x^2 + 7x - 3 - 2x^2 - 7x + 5 \]
Now, combine like terms:
- For \(x^2\) terms: \(4x^2 - 2x^2 = 2x^2\)
- For \(x\) terms: \(7x - 7x = 0\)
- For the constant terms: \(-3 + 5 = 2\)
Putting it all together, we get:
\[ 2x^2 + 0 + 2 = 2x^2 + 2 \]
Therefore, the expression that models the remainder of Alex's workshop space is:
\[ \boxed{2x^2 + 2} \text{ square feet} \]