Answer:
The length of the box is (x+4).
Step-by-step explanation:
The volume of a rectangular prism is represented by the function
[tex]f(x)=x^3+11x^2+20x-32[/tex]
Rewrite the given function in factored form.
[tex]f(x)=(x-1)(x+8)(x+4)[/tex]
It is given that the width of the box is x – 1 while the height is x + 8.
The volume of a rectangular prism is
[tex]V=l\times b\times h[/tex]
where, l is length, b is width and h is height.
Divide both sides by bh.
[tex]\frac{V}{bh}=l[/tex]
Substitute the value of volume, height and width.
[tex]\frac{(x-1)(x+8)(x+4)}{(x-1)(x+8)}=l[/tex]
Cancel out the common factors.
[tex](x+4)=l[/tex]
Therefore the length of the box is (x+4).
