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The box has a height of x inches and a width of (x + 1) inches,The volume of the box is (x^3 + 8x^2 + 7x).  Find the length of the box.

 

 Mar 9, 2021
 #1
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since the volume is height x length x width, 

we can find the length by diving the volume by the width x height.

this means:
length = \(\frac{x^3 + 8^2 + 7x}{(x + 1)(x)}\)

\(= \frac{x(x^2 + 8x + 7)}{x(x + 1)}\)

\(= \frac{x^2 + 8x + 7}{x + 1}\)

\(=\frac{(x + 1)(x + 7)}{x + 1}\)

\(= (x + 7)\)

 

This means the length of the box is (x + 7) inches

 

Hope this helps :)

 Mar 9, 2021

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