HW HELP: please answer all 6 questionsThank you!!

Module 2: Graphs of Polynomial and Rational Functions Topic 3 Application: Real Zeros of Polynomials (2 pages) Using your knowledge of polynomials, provide the correct answers to the following questions in the scenario below. Make sure to completely answer each question and show all of your work. Building a Better Box The economy of the United States depends upon the efficient distribution of consumer goods. Many goods are shipped from manufacturing plants to retail locations by cardboard boxes. In order to not waste cardboard, or otherwise incur unnecessary shipping expenses, manufacturers and retailers look to optimize their cardboard containers. The Real Goods Company (RGC) regularly ships goods from its manufacturing plant to its stores in cardboard boxes. A new product requires a box with a volume of 100 cubic inches (in'). RGC wants to use its existing cardboard stock to make the new box, which imposes these restrictions: the width must be 3 inches greater than the length; and the height must be twice the width. 1. Determine a polynomial function to model the volume of a cardboard box with the stated restrictions in its dimensions; ignore the given volume for this part. (Reminder: the volume of a rectangular prism is / x w x h.) (2 points) 2. Using your function and the given volume, write the equation which determines the dimensions of the new cardboard box (volume = 100 in'). (2 points) 3. Use Descartes Rule to determine the number of positive real number zeros for your equation. (2 points) 4. Use the Rational Zero (Root) Theorem to find all of the possible positive rational zeros of the function (since dimensions are positive, you only need to show the positive values). | (2 points) 5. Find the positive rational real zero(s) of your equation. (2 points) 1 vhro DUCATION Determine the values of s and t so that the remainder is zero when you divide x4 - x3 - 13x2 + sx + t by (x + 3)(x + 4). (2 points)