Unit 2 Description & Learning Goals
In this unit, you will explore the algebraic and geometric properties of polynomial functions of degree three and higher. You will learn to analyze and graph polynomial functions, perform polynomial division, and apply the Remainder and Factor Theorems to simplify and factor expressions. You will use these techniques to solve polynomial equations and inequalities, interpret your solutions, and connect algebraic methods with the graphical behaviour of polynomial functions, including zeros, turning points, and end behaviour.
Key Learning Goals: We are learning
- The algebraic and geometric structure of polynomial functions of degree three and higher
- Algebraic techniques for dividing one polynomial by another
- Techniques for using division to FACTOR polynomials
- To solve problems involving polynomial equations and inequalities
Overall Expectations: (from Ontario Curriculum)
D1. demonstrate an understanding of average and instantaneous rate of change, and determine, numerically and graphically, and interpret the average rate of change of a function over a given interval and the instantaneous rate of change of a function at a given point;
D2. determine functions that result from the addition, substraction, multiplication, and division of two functions and from the composition of two functions, describe some properties of the resulting functions, and solve related problems;
D3. compare the characteristics of functions, and solve problems by modelling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques.