A box is the shape of a rectangular prism. It's volume is given as x^3-2x^2+x. Determine the dimensions.

- A box is the shape of a rectangular prism.
- It's volume is given as x^3-2x^2+x.
- Determine the dimensions of the box.
-Please show all steps in the answer.

V = (length)(width)(depth)

V = x³ - 2x² + x
V = x(x² - 2x + 1)
V = x(x - 1)(x - 1)

Dimensions:
x by (x - 1) by (x - 1)

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One possible solution is found by factoring the expression:

x^3 - 2x^2 + x = x(x-1)(x-1)

So, the dimensions of the box may be x by (x-1) by (x-1). Note that the volume cannot be negative so x >= 1. (The volume is 0 unless x > 1.)

Looks like the dimensions are L, W, H: X(X-1)(X-1)

You just factor into prime factors, the product that was given.

Without knowing the remainder of the equation, I don't understand how to solve the problem.

V = x(x^2 - 2x + 1) = x(x-1)(x-1)

L = x
W= x - 1
H = x - 1