Question

The volume of a rectangular prism is 2x^3+9x^2-8x-36 with height x+2 Using synthetic division, what is the area of the base?

Answer 1

`(2x^3+9x^2-8x-36)/(x+2)=2x^2+5x-18`

Answer 2

`\text{Area of base of prism}=2x^2+5x-18`

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}=\frac{\text{Volume}}{\text{Height}}`

`\text{Area of base of prism}=(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`