Question

A box is created from a sheet of cardboard 40in. on a side by cutting a square from each corner and folding up the sides. let x represent the lenght pf the sides of squares removed from each corner.

What are the factors of this polynomial?

Answer 1

Explanation:

Given that,

A box is created from a sheet of cardboard 40in. on a side by cutting a square from each corner and folding up the sides.

Let x represent the length of the sides of squares removed from each corner.

(a) The volume of a cuboid is given by :

V = lbh

Put values,

V = x(40-2x)(40-2x)

(b) (40-2x) = -2(x-20)

So,

V = x(40-2x)(40-2x)

=
`4x\left(x-20\right)^2`

(c)
`4x\left(x-20\right)^2=4x^3-160x^2+1600x`

It is a cubic polynomial. Its degree is 3.