## Reflection: Developing a Conceptual Understanding Higher Degree Polynomials, Day 1 of 2 - Section 2: Reading Graphs of Polynomials

It's important in this assignment that the students are not given equations.

Algebra is about the interplay between equations, tables of data, and graphs as these are used to define or describe the relationship between two quantities (x and y).  But too often, we restrict ourselves to just one approach; we begin with an equation, we use the equation to produce a table of data, and then we use the data to produce a graph.

When working with these theorems, it's important to take a different starting position. If the equations are given, then the theorems are not as useful.  Their power becomes apparent when students see how much the theorems can tell them about the function without knowing the equation.

Further, many students take for granted that an equation is always available.  It doesn't occur to them that there may be times when the relationship between two quantities isn't fully known, when a data table or a rough graph may be all they have access to.  In these cases, the Remainder Theorem and the Fundamental Theorem can help them to model the relationship with an appropriate polynomial.

Take time to have a conversation with your students about these things.  You might be surprised how much they appreciate it and how deeply they can think about it.

No Equations Necessary
Developing a Conceptual Understanding: No Equations Necessary

# Higher Degree Polynomials, Day 1 of 2

Unit 4: Higher-Degree Polynomials
Lesson 5 of 8

## Big Idea: Applying the Remainder Theorem and the Fundamental Theorem of Algebra, students explore the graphs of higher-degree polynomials.

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Standards:
Subject(s):
Math, polynomial functions, Graphing (Algebra), fundamental theorem of algebra, Algebra 2, master teacher project, Remainder Theorem, Polynomial, Polynomial Operations and Functions
45 minutes

### Jacob Nazeck

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