Question

A rectangular piece of cardboard that is 7 inches by 20 inches has squares of length x inches on a side cut from each corner.

(Assume that 0 < x < 3.) Represent the remaining area in the form of a polynomial function A(x).

Answer 1

The remaining area in the form of a polynomial function
`A(x)= 140-4x^2`where 0 < x < 3.

Explanation:

Breadth of rectangular piece of cardboard = 7 inches

Length of rectangular piece of cardboard = 20 inches

Area of cardboard =
`Length * Breadth`

Area of cardboard =
`20 * 7`

Area of cardboard =
`140 in^2`

Squares of length x inches on a side cut from each corner.

Length of square = x

Area of 1 square =
`Side^2 = x^2`

Area of 4 squares =
`4x^2`

Area of remaining portion
`A(x)= 140-4x^2`

So, the remaining area in the form of a polynomial function
`A(x)= 140-4x^2`where 0 < x < 3.