SOLUTION: This is an application problem using polynomial equations/functions: "An open box with a rectangular base is to be made from a rectangular piece of cardboard by cutting out a squa

Question 1095380: This is an application problem using polynomial equations/functions: "An open box with a rectangular base is to be made from a rectangular piece of cardboard by cutting out a square of x inches from each corner and turning up the sides. The dimensions of the cardboard are 25 inches by 20 inches. Write a function in one variable for the volume of the box."
I assume the dimensions given are for the cardboard prior to the squares being cut from each corner, so this is what I came up with:
V = lwh
l = 25 - 2x
w = 20-2x
h = x
so:
f(x) = (25-2x)(20-2x)x
f(x) = 4x^3 - 90x^2+500x
But I'm pretty sure this is incorrect. I'm stumped. Can you show me where I've gone wrong?
Thank you for any help you can give me.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

You are "pretty sure" your work is incorrect...

I am POSITIVE that you are mistaken there.

Your work is exactly what it should be.
Note that there is no need to expand the formula into a polynomial form; the factored form is sufficient, and for many applications would even be more meaningful and therefore better.
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