Use the written statement to construct a polynomial function

Question

Use the written statement to construct a polynomial function that represents the required information.

A rectangle is twice as long as it is wide. Squares with sides measuring 4 feet are cut out from each corner. Then the sides are folded up to make an open box. Express the volume V of the box as a function of the width x, where V is measured in square feet.
V(x) =

 

?x^2-?x+?

Answer 1

w represents the width

2w represents the length

 

V = 4(w - 8)(2w - 8)

 

Can you multiply out and answer?

Answer 2

Let width of rectangle = x

Let length of rectangle = 2x

 

width of base of box = x - 2(4) = x - 8

length of base of box = 2x - 2(4) = 2x - 8

height of box = 4

 

Then the formula for volume of box is

 

V = 4(2x - 8)(x - 8)

V = 4(2x² - 24x + 64)

V = 8x² - 96x + 256