Final answer:
The standard form of the polynomial representing the width of the highway cannot be determined with the information provided as it requires subtracting both x (one building's distance from the highway) and y (the other building's distance from the highway) from the total distance between the buildings. None of the answer choices account for the variable y.
Step-by-step explanation:
The standard form of the polynomial that represents the width of the highway between the two buildings would be found by subtracting the distances of both buildings from the highway from the total distance between the two buildings. If one building is x feet from the highway, and the other building is y feet from the highway, then the distance between the two buildings minus these two distances would give us the width of the highway.
Therefore, the polynomial for the width of the highway is (3x³ - x² + 7x + 100) - x - y. Since we do not have the value of y, we cannot simplify this expression further without additional information. Consequently, none of the given answer options - 1) 3x³ - x² + 7x + 100, 2) 3x³ - x² + 7x - 100, 3) -3x³ + x² - 7x + 100, 4) -3x³ + x² - 7x - 100 - correctly represent the width of the highway since all options ignore the value of y, the distance one of the buildings is from the highway.