Question

A rectangular prism has length that is twice its width and height that is 4 meters longer than its width. the volume of the rectangular prism is 48 cubic meters write a polynomial function to represent the volume of the rectangular prism

Answer 1

Let
x-----------> is the length of a prism
y-----------> is the width of a prism
z-----------> is the height of a prism

we know that
[volume of a prism]=x*y*z------------> equation 1
x=2y-----------> equation 2
z=4+y---------> equation 3
V=48 m³

I substitute 2 and 3 in 1
V=x*y*z---------> V=(2y)*y*(4+y)--------> V=2y²*(4+y)
V=2y³+8y²-----------> 48=2y³+8y²---------> 2y³+8y²-48=0

the answer is
2y³+8y²-48=0  (polynomial function)

using a graph tool
see the attached figure

y=2 m
x=2y------->x=2*2-----> x=4 m
z=4+y-------> z=4+2-----> z=6 m