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

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

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

$\text{Thus, Area of base of prism is }2x^2+5x-18$

Answer 2

$\dfrac{2x^3+9x^2-8x-36}{x+2}=2x^2+5x-18$