Answer: the polynomial representing the shaded region is
2x² - 6x - 1
Step-by-step explanation:
The area of the square is expressed as 4x² - 2x - 6
The area of the triangle is expressed as 2x² + 4x - 5. The area of the shaded region would be the area of the square - the area of the area of the triangle.
The polynomial that represents the area of the shaded region would be
4x² - 2x - 6 - (2x² + 4x - 5)
Collecting like terms, it becomes
= 4x² - 2x² - 2x - 4x - 6 + 5
= 2x² - 6x - 1
