Name:_________________________ MHF4UE Unit 1 Part 1: Polynomial Functions - Thinking Task [12 marks] This is an evaluation that must be completed on your own with no help from tutors, friends or the internet. To earn full marks, you must justify your solution. Include the following as needed: Show diagram, Define variables, State formula, theorem, equation or function used, Show substitutions and or steps in solving an equation, State restrictions, State concluding statement, Use correct notation. No marks are given if your solution includes: e or ln, differentiation, integration. 1. The revenue, 𝑅(𝑥), in thousands of dollars, from ticket sales for a local theatre production over time is modelled by the function 𝑅(𝑡) = 2(𝑡 − 2)(𝑡 − 3)(𝑡 + 5), where t represents the number of weeks since ticket sales opened, 𝑡 ∈ [0, 10]. Determine when the revenue reaches $120,000. Solve algebraically, showing all steps clearly to receive full marks. [7 marks] Name:_________________________ 3 2 MHF4UE 2. The polynomial 𝑓(𝑥) = 𝑝𝑥 + 12𝑥 + 𝑞𝑥 − 40 has a factor of (𝑥 + 2) and a remainder of 20 when divided by (𝑥 − 3). Find the values of 𝑝 and 𝑞. Reference any relevant theorems to support your reasoning. Show all steps for full marks. [5 marks]