Dashboard | Colorado Virtual A X 5 Alg2_M3_3.4.pdf X Copy of P BMF U1 A- AT - Goo! X Homework Help - Q&A from Or x Premier Membership Upgrade x C A s3.amazonaws.com/content.accelerate-ed.com/Secondary/docs/Algebra2ew_assets/worksheets/Alg2_M3_3.4.pdf Update : E Alg2_M3_3.4.pdf 1 / 2 100% + Module 3, Polynomials Assignment Polynomials are everywhere in the world around you! From roller coaster and bridge design, to economic growth patterns, to supermarket inventory management and more, you can find polynomials everywhere you look! Since polynomials can be used to model so many phenomena in our world, mathematicians have developed several theorems to help us. Two of these theorems are listed below. The Remainder Theorem The Factor Theorem If you divide a polynomial P(x) by (x - A polynomial P(x) has a factor (x - a) if a), then the remainder is P(a). and only if P(a) = 0. Think about these theorems as you consider the application of polynomials below. 2 An animal sanctuary is constructing a large tank for its exotic fish collection. The tank will be a rectangular prism that is set into a large wall, and it will feature two, equally-sized hemispheres, one on each side of the tank. Visitors will be able to sit inside these hemispheres so they can feel like they are inside the tank with the fish. The polynomial (2x - 30) represents the length of the new tank, the polynomial (2x - 20) represents the width of the new tank, and the polynomial (2x - 60) represents the height of the new tank. Use the information given to explore some of the mathematical concepts you have practiced so far by answering the questions below.Dashboard | Colorado Virtual A X 5 Alg2_M3_3.4.pdf X Copy of P BMF U1 A- AT - Goo X * Homework Help - Q&A from Or x Premier Membership Upgrade x C A s3.amazonaws.com/content.accelerate-ed.com/Secondary/docs/Algebra2ew_assets/worksheets/Alg2_M3_3.4.pdf Update : Alg2_M3_3.4.pdf 2 / 2 100% + 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 x5 - 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. 2 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