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BARSIC [14]
3 years ago
7

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.)
Mathematics
1 answer:
EastWind [94]3 years ago
8 0
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 / <span>3n + 1
You can do this division by factoring, synthetic division, or by plain division.
Factoring out 3n + 1 from the numerator gives you:
</span>s² = (3n + 1)(n² + 4n + 4) / 3n+1
s² = n² + 4n + 4

Therefore, the area of the square base is <span>n² + 4n + 4.</span>
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