Name:_________________________ MHF4UE Unit 1 Part 1: Polynomial Functions - Communication Task [9 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. 2 4 2 1. Knowing that 𝑥 + 5𝑥 + 6 is a factor of 𝑥 + 𝑟𝑥 + 𝑠 , find the values of coefficients without using long or synthetic division. Describe the steps of your solution using mathematical terminology stating any theorems learned in this unit. [5] Name:_________________________ 2. Sketch a graph of a fifth degree polynomial 𝑓(𝑥) such that 𝑓(𝑥) < 0 when 𝑥 <− 4, − 4 < 𝑥 < 2, and 2 < 𝑥 < 5. Explain, in words, the steps taken to sketch the graph. MHF4UE [4]