The dimensions of a rectangular prism are n, n + 7, and n + 8. Use the formula V = l ∙ w ∙ h to write a polynomial in standard form for the volume of the prism.
The volume formula for a rectangular prism is V = l ∙ w ∙ h. Given that the dimensions of the prism are n, n + 7, and n + 8, we can substitute these values into the formula:
V = n(n + 7)(n + 8)
Expanding the terms:
V = n(n^2 + 8n + 7n + 56)
V = n(n^2 + 15n + 56)
V = n^3 + 15n^2 + 56n
Therefore, the polynomial in standard form for the volume of the prism is V = n^3 + 15n^2 + 56n.