Answer:
the missing side length is [tex](2x+5)[/tex]
Step-by-step explanation:
we know that the volume of the rectangular prism is equal to
[tex]v=LWH[/tex]
In this problem we have
[tex]v=L(x+4)(x+2)[/tex]
[tex]v=2x^3+17x^2+46x+40[/tex]
using a graphing tool find the x-intercepts of the function
see the attached figure
The x-intercepts are
[tex]x=-4, x=-2.5, x=-2[/tex]
so
[tex]v=2(x+2.5)(x+4)(x+2)[/tex]
[tex]v=(2x+5)(x+4)(x+2)[/tex]
therefore
the missing side length is [tex](2x+5)[/tex]
