Answer: The required answer is [tex]2x^2-5x-5.[/tex]
Step-by-step explanation: We are given to divide the following algebraic fraction :
[tex]F=\dfrac{-4x^3+35x+25}{-2x-5}.[/tex]
We will try to write the cubic numerator as a product of a linear factor (denominator) and a quadratic factor.
The simplification is as follows :
[tex]F\\\\=\dfrac{-4x^3+35x+25}{-2x-5}\\\\\\=\dfrac{-(4x^3-35x-25)}{-(2x+5)}\\\\\\=\dfrac{4x^3-35x-25}{2x+5}\\\\\\=\dfrac{2x^2(2x+5)-5x(2x+5)-5(2x+5)}{2x+5}\\\\\\=\dfrac{(2x+5)(2x^2-5x-5)}{(2x+5)}\\\\=2x^2-5x-5.[/tex]
Thus, the required answer is [tex]2x^2-5x-5.[/tex]
