To find the area of the final polygon after combining the given polygon and rectangle and removing another polygon, we need to follow the given steps.
Step 1: Find the area of the combined polygon and rectangle.
The area of the combined polygon and rectangle is obtained by adding the individual areas. The area of the combined shape will be (2x^2 + 5x - 10) + (length * width), where the length is (x - 7) units and the width is (3x + 4) units.
Therefore, the area of the combined polygon and rectangle is:
(2x^2 + 5x - 10) + (x - 7)(3x + 4)
Step 2: Subtract the area of the second polygon.
To find the final area, we need to subtract the area of the second polygon, which is (3x^2 - 25x - 8) square units.
Final area = (2x^2 + 5x - 10) + (x - 7)(3x + 4) - (3x^2 - 25x - 8)
Now we can simplify and combine like terms to find the final area.
If you have any specific values for x that you would like to use in this calculation or if you need further assistance, please let me know!