The formula for volume of this rectangular prism is:V = 2x 3 + 17x 2 + 46x + 40Find an expression for the missing side length. Show all of your work for full credit.

 By definition, the volume of a rectangular prism is given by:
 [tex]V = (w) * (h) * (l) [/tex]
 Where,
 l: length
 h: height
 w: width
 Substituting values we have:
 [tex]2x ^ 3 + 17x ^ 2 + 46x + 40 = (w) * (x + 2) * (x + 4) [/tex]
 From here, we clear the value of w.
 [tex]w = (2x ^ 3 + 17x ^ 2 + 46x + 40) / ((x + 2) * (x + 4)) [/tex]
 Factoring the numerator we have:
 [tex]w = ((x + 2) * (x + 4) * (2x + 5)) / ((x + 2) * (x + 4)) [/tex]
 Canceling similar terms we have:
 [tex]w = 2x + 5 [/tex]
 Answer:
 The missing side is of length:
 w = 2x + 5