Question

Use your knowledge of polynomials to help the company design the box for one of its products.

Answer 1

Answer:

(a) The area of the sheet is (9x² - 12x + 4).

(b) The total surface area of the box is x (5x - 4) inches².

Step-by-step explanation:

It is provided that the width and the length of the box are x inches and the height of the box is (x - 1) inches

Then the width of the sheet is:

Width of sheet = (x - 1) + x + (x - 1)

                         = x - 1 + x + x - 1

                         = 3x - 2

(1)

The area of the sheet is:

Area of sheet = (3x - 2)² =

                       = (3x)² - 2 · 3x · 2 + (2)²

                       = 9x² - 12x + 4

Thus, the area of the sheet is (9x² - 12x + 4).

(2)

The central area, i.e. the base of the box = x²

Each arm folded up = x by (x - 1)

Then the areas of the 4 arms = 4 · x · (x - 1) = 4x² - 4x

Then the total surface area is:

Total Surface Area = Central Area + Areas of the 4 arms

                                = (x²) + (4x² - 4x )

                                 = 5x² - 4x

                                = x (5x - 4) inches²

Thus, the total surface area of the box is x (5x - 4) inches².