A rectangular box has the dimensions shown in the diagram. The volume of the box is given by the function V(x) = x3 – 4x, where x is the height in inches. What is the height of the box if the volume is 15 in.3?

length, width, and height are (b+2), (b-2), (b+3)

Step-by-step explanation:

Doing what the problem statement tells you to do, you get ...

(b^3 +3b^2) -(4b +12)

= b^2(b +3) -4(b +3) . . . . . factor each pair of terms

= (b^2 -4)(b +3) . . . . . . . . . write as a product

= (b -2)(b +2)(b +3) . . . . . . use the factoring of the difference of squares

The three factors are (b-2), (b+2), and (b+3). We have no clue as to how to associate those with length, width, and height. We just know these are the dimensions of the box.

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step-by-step explanation:

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