Answer:
\(\text{Area of base of prism}=2x^2+5x-18\)
Step-by-step explanation:
Given:
Volume of a rectangular prism is \(2x^3+9x^2-8x-36\)
Height of prism is x+2
We need to find the area of base of prism.
\(\text{Area}=\dfrac{\text{Volume}}{\text{Height}}\)
\(\text{Area of base of prism}=\dfrac{2x^3+9x^2-8x-36}{x+2}\)
Using synthetic division,
-2 | 2 9 -8 -36 |
-4 -10 36
2 5 -18 0
Now we make polynomial
\(\text{Area of base of prism}=2x^2+5x-18\)
\(\text{Thus, Area of base of prism is }2x^2+5x-18\)
