The height of a square prism is 3n + 1. The volume of the prism is 3n³ + 13n² + 16n + 4. What is the area of the square base of the prism? (Show all steps.)

If s is the side of the square base, the area of the square base is s^2.

The volume of the square base is,

V = (s²) (h)

s² = V/h

s² = 3n³ + 13n² + 16n + 4 / 3n + 1

You can do this division by factoring, synthetic division, or by plain division.

Factoring out 3n + 1 from the numerator gives you:

s² = (3n + 1) (n² + 4n + 4) / 3n+1

s² = n² + 4n + 4

Therefore, the area of the square base is n² + 4n + 4.