Question 47150
To make a box from a 18 by 20 inch piece of cardboard, you would need to cut the corners from the piece.  Let's say that you cut an x by x square from each corner of the given piece of cardboard so that you could then fold the sides up to form an open box. The volume of the resulting box can be expressed by the following polynomial function of x:
{{{V = x(18-2x)(20-2x)}}}
{{{V = 360x-36x^2-40x^2+4x^3}}} Simplify.
{{{V = 4x^3-76x^2+360x}}} This is the polynomial function.

The graph looks like this:
{{{graph(300,200,-5,15,-20,500,4x^3-76x^2+360x)}}}

If the volume is to equal 224 cubic inches, the equation would be:

{{{4x^3-76x^2+360x = 224}}} Subtract 224 from both sides.
{{{4x^3-76x^2+360x-224 = 0}}} Simplify by dividing through by 4.
{{{x^3-19x^2+90x-56 = 0}}} Solve for x 

The 3 solutions are:
x = 0.73
x = 6.53
x = 11.74