The volume in cubic feet of a workshops storage chest can be expressed as the product of its three dimensions : V(x)=x^3+4x^2-11x-30. The length is (x+2).
1)what is the actual volume of the storage chest in cubic feet ?show 2 ways to find your answer

Question

The volume in cubic feet of a workshops storage chest can be expressed as the product of its three dimensions : V(x)=x^3+4x^2-11x-30. The length is (x+2).
1)what is the actual volume of the storage chest in cubic feet ?show 2 ways to find your answer

mathmale · Answer

The volume of the chest is dependent upon the value of the variable x.  If, for example, x=2, then the actual volume of the chest would be V(x)=x^3+4x^2-11x-30 with 2 substituted for x.

Given that the formula for the total volume is provided in this question, you could simply repeat that formula to obtain the volume in its most general case.

Alternatively, if the length is (x+2), you could divide that into the formula for volume.  The result would be the product of the width and the height of the box.  You might be able to factor this further, or you might not.  You could then write the volume formula as
$$V(x) = (x+2)*(quotient~ of~V(x)~ and ~(x+2))$$

mathmale · Answer

...but I'm not sure that's worth the effort!