Question

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.)

Answer 1

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.