Answer:
5x-1.
Step-by-step explanation:
We have been the formula for the volume of a rectangular prism as: [tex]V = 5x^3+29x^2+34x-8[/tex] 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.
[tex]\text{Missing side}=\frac{5x^3+29x^2+34x-8}{(x+2)(x+4)}[/tex]
[tex]\text{Missing side}=\frac{5x^3+29x^2+34x-8}{x^2+6x+8}[/tex]
[tex]\text{Missing side}=\frac{(5x-1)(x^2+6x+8)}{x^2+6x+8}[/tex]
[tex]\text{Missing side}=(5x-1)[/tex]
Therefore, missing length of the rectangular prism is 5x-1.
