The length of a box is 2 centimeters less than its height. the width of the box is 7 centimeters more than its height. How do you write a polynomial that represents the volume of the box?

Sep 26, 2016

Let the the height be $x$. Then the width is given by $x + 7$ and the length is given by $x - 2$.

$V = l \times w \times h$

$V = \left(x - 2\right) \left(x + 7\right) \left(x\right)$

$V = \left({x}^{2} - 2 x + 7 x - 14\right) \left(x\right)$

$V = \left({x}^{2} + 5 x - 14\right) \left(x\right)$

$V = {x}^{3} + 5 {x}^{2} - 14 x {\text{ cm}}^{3}$

Hopefully this helps!