Answer:
[tex]V(x) = 4x^3 - 54x^2 + 180x[/tex]
Step-by-step explanation:
We are given the following in the question:
A rectangular piece of cardboard of side 15 inches by 12 inches is cut in such that a square is cut from each corner.
Let x be the side of this square cut. When it was folded to make the box.
The height of box =
[tex]x\text{ inches}[/tex]
The length becomes
[tex](15-2x)\text{ inches}[/tex]
The width becomes
[tex](12-2x)\text{ inches}[/tex]
Volume of box =
[tex]V =l\times w\times h[/tex]
Putting values, we get
[tex]V(x) = (15-2x)(12-2x)x\\V(x) = (180-30x-24x+4x^2)(x)\\V(x) = (4x^2 - 54x + 180)(x)\\V(x) = 4x^3 - 54x^2 + 180x[/tex]
is the required polynomial for volume of box formed.
