Please help. I have tried many times to come up with something after reading the material but I am completely stumped.

A cubic container, with sides of length, x inches, has a volume equal to x^3 cubic inches. The height of the container was decreased and the length was increased so that the volume is now modeled by the expression

x^3+4x^2-5x

By how many feet were the height and length changed?
(Hint: Volume = length times width times height)

your new expression factors to

x(x+5)(x-1)

so I would say the length was increased by 5, the width remained the same and the height was shortened by 1

To solve this question, we need to find the change in height and length of the container.

The given expression represents the new volume of the container: x^3 + 4x^2 - 5x.

We know that the volume of a rectangular container is given by the formula: Volume = length * width * height.

In this case, the length and width are equal, so we can use the same variable, x, for both of them. Thus, the equation becomes: Volume = x * x * height = x^2 * height.

We can set the initial volume of the container (before any changes) equal to the new volume:

x^3 = x^2 * height.

Dividing both sides of the equation by x^2, we get:

x = height.

So, the initial height of the container was x inches.

Now, let's look at the new volume expression: x^3 + 4x^2 - 5x.

Since the initial height was x inches, we can substitute it into the expression:

x^3 + 4x^2 - 5x = x^2 * x + 4x^2 - 5x = x^3 + 4x^2 - 5x.

We can see that the new volume expression is the same as the initial volume expression. It means that there was no change in the dimensions of the container. Therefore, the height and length were not changed.

In conclusion, the height and length of the container were not changed; they remained the same.