Question

A wild animal generally stays at least x mi from the edge of a forest. For a rectangular forest preserve that is 2 mi

long and 5 mi wide, write a polynomial that represents the area of the available habitat for the wild animal.
(Note: diagram not drawn to scale)

Answer 1

`Area = 4x^2 - 14x + 10`

Explanation:

See Attachment for Complete Question

Given

`Width = 5mi` --- For the forest

`Length = 2mi` -- --- For the forest

Required

Determine the area of the habitat

Since the distance between the animal's habitat is x mi on both sides;

The length and width of the habitat is:

`Width = 5 - (x + x)`

`Width = 5 - 2x`

`Height = 2 - (x +x)`

`Height = 2 - 2x`

The area is then calculated as follows;

`Area = Width * Height`

`Area = (5 - 2x) * (2 - 2x)`

Expand

`Area = 5(2 - 2x) -2x(2 - 2x)`

Open Brackets

`Area = 10 - 10x - 4x + 4x^2`

`Area = 10 - 14x + 4x^2`

Reorder

`Area = 4x^2 - 14x + 10`

Hence; the required polynomial for the habitat area is:

`Area = 4x^2 - 14x + 10`