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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?

Answer 1

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 expresses the prism's volume and is a polynomial

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.