Answer:
[tex]Volume = x^3 +3x^2 -16x +12[/tex]
Step-by-step explanation:
Given [missing from the question].
The dimensions are:
Length =(x + 6), Width = (x - 2) and Height = (x -1)
Required
Represent the volume as a polynomial
Volume is calculated as:
[tex]Volume = Length * Width * Height[/tex]
So:
[tex]Volume = (x + 6) * (x - 2) * (x - 1)[/tex]
Expand
[tex]Volume = (x + 6) * (x^2 -2x -x +2)[/tex]
[tex]Volume = (x + 6) * (x^2 -3x +2)[/tex]
Expand
[tex]Volume = x^3 -3x^2 +2x +6x^2-18x +12[/tex]
Collect like terms
[tex]Volume = x^3 -3x^2+6x^2 +2x -18x +12[/tex]
[tex]Volume = x^3 +3x^2 -16x +12[/tex]
