# The volume of a rectangular prism is 3x^3+34x^2+72x-64, if the height is x+4, what is the area of the base of the prism?

Feb 7, 2017

$3 {x}^{2} + 22 x - 16$ square units.

#### Explanation:

The formula for volume of a prism is $V = {A}_{\text{base}} \cdot h$. Therefore,

$3 {x}^{3} + 34 {x}^{2} + 72 x - 64 = \left(x + 4\right) {A}_{\text{base}}$

${A}_{\text{base}} = \frac{3 {x}^{3} + 34 {x}^{2} + 72 x - 64}{x + 4}$

Use either synthetic or long division. I will use long division but either methods work.

Therefore, the quotient is $3 {x}^{2} + 22 x - 16$. This means the area of the base is $3 {x}^{2} + 22 x - 16$ square units.

Hopefully this helps!