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.
2. The volume of each hemisphere is represented by the polynomial x3 - 70x2 + 360x - 1800.
Explain how to rewrite your answer for question 1 to reflect the volume of the fish tank after the
hemispheres are installed. Then carry out your plan. Show your work.
3. Show that the binomial that represents the length of the fish tank is a factor of the polynomial
you wrote in question 1.
4. Is the binomial that represents the length of the fish tank a factor of the polynomial that
represents the volume of the fish tank after the hemispheres are installed? Support your answer
mathematically.
5. The sanctuary currently has 125 exotic fish. The average amount of the tank allotted for each
fish is represented by the binomial (2x2 - 1). Are the dimensions of the new habitat adequate
for these 125 fish? Explain.