The problem is to divide the polynomial $88x^5 + 66x^3 - 52x^2$ by $-2x^2$.

1. Problem Description

The problem is to divide the polynomial $88x^5 + 66x^3 - 52x^2$ by $-2x^2$.

2. Solution Steps

We will divide each term of the polynomial $88x^5 + 66x^3 - 52x^2$ by $-2x^2$.

$\frac{88x^5}{-2x^2} = -44x^{5-2} = -44x^3$

$\frac{66x^3}{-2x^2} = -33x^{3-2} = -33x$

$\frac{-52x^2}{-2x^2} = 26x^{2-2} = 26$

Adding these terms gives the result of the division.

3. Final Answer

The final answer is $-44x^3 - 33x + 26$.