Step 1 :The problem is asking for the quotient when the polynomial \(-4w^3 + 4w^2 - 5\) is divided by \(w - 3\). This is a simple polynomial division problem.
Step 2 :We can solve this by using the synthetic division method or long division method for polynomials.
Step 3 :Performing the division, we find that the quotient is \(-4w^2 - 8w - 24\).
Step 4 :Final Answer: The quotient when the polynomial \(-4w^3 + 4w^2 - 5\) is divided by \(w - 3\) is \(\boxed{-4w^2 - 8w - 24}\).