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.
a. 3n + 15
b. 3n + 56
c. n^2 + n + 56
d. n^3 + 15n^2 + 56n
The formula for the volume of a rectangular prism is V = l * w * h.
In this case, the length is n, the width is n + 7, and the height is n + 8.
Substituting these values into the formula, we get:
V = n * (n + 7) * (n + 8)
Expanding this expression:
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:
d. n^3 + 15n^2 + 56n