Adaptive Perseverance: Students will persist through the challenges of simplifying, solving, and graphing polynomials, exploring multiple methods for accurate results.
Learner’s Mindset: Students will demonstrate curiosity and openness to learning different polynomial operations and graphing techniques, seeking continuous improvement.
Communication: Students will articulate their understanding of polynomial operations and graphing clearly, both verbally and in writing.
Responsibility: Students will take responsibility for the accuracy and integrity of their polynomial simplifications, solutions, and graphs, ensuring they meet the required standards.
Critical Thinking: Students will analyze and evaluate different methods for simplifying, solving, and graphing polynomials, applying logical reasoning to interpret and write equations.
What are the steps to simplify polynomials through addition, subtraction, multiplication, and division (both long division and synthetic division)?
How can we solve polynomial equations, and what methods are most effective for different types of polynomials?
How do the degree and leading coefficient of a polynomial function influence its graph and end behavior?
Students will simplify polynomials accurately using addition, subtraction, multiplication, and both long and synthetic division.
Students will solve polynomial equations using appropriate methods and verify their solutions.
Students will graph polynomial functions and identify key properties such as degree, leading coefficient, and end behavior, analyzing how these properties influence the graph.
Students are able to convert quantitative problems that use words into mathematical expressions.
CCSS.MATH.CONTENT.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.
CCSS.MATH.CONTENT.HSA.APR.B.2: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x−a is p(a).
CCSS.MATH.CONTENT.HSA.APR.D.6: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x)+r(x)/b(x) with a(x), b(x), q(x), and r(x) polynomials and the degree of r(x) less than the degree of b(x).
CCSS.MATH.CONTENT.HSF.IF.C.7.C: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
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