Question

The formula for the volume of this rectangular prism is: V = 5x3 + 29x2 + 34x – 8 Find an expression for the missing side length. Show all of your work for full credit.
The lengths are x + 2 and x + 4 find the missing length

Answer 1

Answer:

5x-1.

Step-by-step explanation:

We have been the formula for the volume of a rectangular prism as: $V = 5x^3+29x^2+34x-8$ and the lengths are (x+2) and (x+4).

Since we know that volume of a rectangular prism is length times width times height, so to find the our missing length we will divide volume of rectangular prism by the given side length.

$\text{Missing side}=\frac{5x^3+29x^2+34x-8}{(x+2)(x+4)}$

$\text{Missing side}=\frac{5x^3+29x^2+34x-8}{x^2+6x+8}$

$\text{Missing side}=\frac{(5x-1)(x^2+6x+8)}{x^2+6x+8}$

$\text{Missing side}=(5x-1)$

Therefore, missing length of the rectangular prism is 5x-1.