Critical Thinking: Students analyze and solve problems involving polynomial equations.
Responsibility: Students complete tasks accurately, understanding the importance of precision in mathematical work.
Adaptive Perseverance: Students apply multiple strategies to understand and solve polynomial equations.
Learner’s Mindset: Students seek to understand complex concepts in polynomials and their applications.
How do operations with polynomials (addition, subtraction, multiplication) mirror operations with numbers, and how are they different?
In what situations can factoring polynomials simplify solving complex equations, and why is it useful?
How can understanding polynomial equations help us model and solve real-world problems, such as calculating areas or predicting outcomes?
Students will manipulate polynomials to solve problems.
Students will apply operations with polynomials in various contexts.
Students will factor polynomials as a strategy to solve polynomial equations and apply these skills in problem-solving scenarios.
HSA-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
HSA-APR.B.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
HSA-SSE.A.2: Use the structure of an expression to identify ways to rewrite it. For example, see x⁴ - y⁴ as (x²)² - (y²)², thus recognizing it as a difference of squares that can be factored as (x² - y²)(x² + y²).
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