How do you write a polynomial that represents the volume of a box that is a rectangular prism has the dimensions length x+6, width x-2, and height x-1?

1 Answer
KillerBunny
Feb 4, 2015

The volume of a rectangular prism is simply the product of its three dimensions: in your case, the volume of the prism is, given #x#,

#(x+6)(x-2)(x-1)#.

A polynomial is a sum (with some coefficients) of powers of #x#, so, if we expand the product just written, we have

#((x+6)(x-2))(x-1) = #
#(x^2-2x+6x-12)(x-1) = #
#(x^2+4x-12)(x-1)=#
#x^3+4x^2-12x-x^2-4x+12=#
#x^3 +3x^2-16x+12#

Which is a polynomial, and expresses the volume of the prism

Related questions
See all questions in Applications of Function Models
Impact of this question
48379 views around the world
You can reuse this answer
Creative Commons License