Final answer:
The polynomial representing the remaining area of a deck after installing a 5ft by 7ft Jacuzzi is y^2 - 12y + 35, which considers the area of the Jacuzzi and the reduced deck dimensions.
Step-by-step explanation:
The student is asking for the polynomial that represents the remaining area of the deck after a Jacuzzi that measures 5 feet by 7 feet has been installed on it. If the deck itself is a square with sides of length y feet, the area of the deck is y2. The area of the Jacuzzi is fixed at 5 feet by 7 feet, which equals 35 square feet. To find the remaining area of the deck, we need to subtract the area of the Jacuzzi from the total area of the deck, which gives the expression y2 - 35. However, because the Jacuzzi is being installed on the deck, we have to consider its limits within the length y, hence introducing a linear term involving y. Since the Jacuzzi is positioned on the deck, its sides will reduce the available length and width by 5 feet and 7 feet, respectively. Combining these considerations correctly, the polynomial for the remaining area is found by subtracting both the area of the Jacuzzi and the product of its sides multiplied by y (representing the reduced length and width of the deck), resulting in the polynomial y2 - 12y + 35.