Question

The dimensions of a rectangular prism are n, n + 7, and n + 8. Use the formula V = ewh to write a polynomial in standard form for the volume of the prism

Answer 1

Answer:

n³ + 15n² + 56n

Step-by-step explanation:

The formula for the volume of a rectangular prism is V = l × w × h.

We are given the dimensions of this rectangular prism: n, n + 7, n + 8.

We can assume that these are the length, width, and height of the rectangular prism (not in any specific order).

Let's substitute these values into the formula to find the volume of the prism, written as a polynomial in standard form.

• V = l × w × h
• V = (n) × (n + 7) × (n + 8)
• V = (n² + 7n) × (n + 8)
• V = n³ + 8n² + 7n² + 56n
• V = n³ + 15n² + 56n

The volume of the prism is n³ + 15n² + 56n. This is in standard form because the terms are listed in descending power order.