A2-A-1-4

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A2.A.1.4 Solve polynomial equations with real roots using various methods and tools that may include factoring, polynomial division, synthetic division, graphing calculators or other appropriate technology.

In a Nutshell

Students will learn a variety of methods to solve polynomials equations, including factoring, polynomial and/or synthetic division and technology. They will learn to identify the most efficient method to solve a given polynomial equation.

Student Actions	Teacher Actions
Students will develop a deep and flexible conceptual understanding and can explain the mathematical basis for the relationship between solving for real roots, finding a solution, finding the zeros or finding the x-intercepts. Students will develop strategies for solving polynomial equations by selecting from a variety of problem solving strategies including factoring, division and graphing calculators.	Implement tasks for students to use varied approaches and strategies, such as factoring, polynomial division, and graphing technology, to make sense of and solve polynomial equations. Support students in productive struggle by anticipating what students might struggle with while solving polynomial equations and be prepared to support them productively through the struggle.
Key Understandings	Misconceptions
Identify the standard form of a polynomial. Identify the best method to solve a polynomial equation. Understand the various methods of solving polynomials including factoring, division, and graphing and be able to switch between methods if necessary. Identify solutions of an equation f(x) = 0 as the x-intercepts of the graph of f(x), and know the relationship between solutions, roots, zeros, x-intercepts and factors.	Procedural: Students may try to factor a polynomial that cannot be factored. Students try to use synthetic division when it’s not possible. Students do not put the equation in standard form before solving. The student may forget to use a zero coefficient in place of any missing terms when dividing.