Question

Polynomial: Length=(2x-30) Width=(2x-20) Height=(2x-60) 1. Find a polynomial that represents volume of the fish tank. Explain how you used the properties of exponents to determine your expression.HINT: The formula for the volume of a rectangular prism is V = lwh.

Answer 1

The volumen of the fish tank is:

`\begin{gathered} V=l\cdot w\cdot h \\ l=2x-30=2(x-15) \\ w=2x-20=2(x-10) \\ h=2x-60=2(x-30) \\ V=2\cdot(x-15)\cdot2\cdot(x-10)\cdot2\cdot(x-30) \\ V=8\cdot(x^2-10x-15x+15\cdot10)\cdot(x-30)=8\cdot(x^2-25x+150)(x-30) \\ V=8\cdot(x^3-30x^2-25x^2+25x\cdot30+150x-150\cdot30) \\ V=8\cdot(x^3-55x^2+900x-4500) \\ V=8x^3-440x^2+7200x-36000 \end{gathered}`