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