Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.7

Prove polynomial identities and use them to describe numerical relationships.

COS Examples

Example: The polynomial identity $1 - x^n = (1 - x)(1 + x + x^2 + x^3 + … + x^{n-1} + x^n)$ can be used to find the sum of the first n terms of a geometric sequence with common ratio x by dividing both sides of the identity by $(1 - x)$.

Unpacked Content

Knowledge

Students know:
  • Distributive Property of multiplication over addition.

Skills

Students are able to:
  • Accurately perform algebraic manipulations on polynomial expressions.

Understanding

Students understand that:
  • Reasoning with abstract polynomial expressions reveals the underlying structure of the Real Number System.
  • Justification of generalizations is necessary before using these generalizations in applied settings.

Vocabulary

  • Polynomial Identity
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