A cubic container, with sides of length, x inches, has a volume equal to x3 cubi

Question

A cubic container, with sides of length, x inches, has a volume equal to x3 cubic inches. The height of the container was decreased and the length was increased so that the volume is now modeled by the expression

x3+4x2-5x

? By how many feet were the height and length changed?
(Hint: Volume = length times width times height)

Explanation / Answer

To determine the dimensions of the container you need to write the volume as the result of a multiplication hence: x^3+4x^2-5x=x(x^2+4x-5) = x(x+...)(x+...) Using the distributive law, you see that the three brackets yield x^3, which is part of the given expression of the volume There are two ways to get a product of two numbers to be -5: 1*-5 and -1*5 Put 1 into the first empty spot in the equation above and -5 into the second empty spot and use the distributive law to check the result: -->x(x+1)(x-5) =x(x^2+x-5x-5)=x(x^2-4x-5) This is not the desired result So try the other option: Put -1 into the first empty spot and 5 into the second empty spot and use the distributive law to check the result: --> x(x-1)(x+5) = x(x^2-x+5x-5)=x(x^2+4x-5) This is the desired result Since volume = length times width times height, width decreased by 1 and height increased by 5.

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