What the learner will study

• Polynomial Vocabulary, Degree & Structure
• Polynomial Operations & Equivalent Forms
• Power Functions & End Behavior
• The Imaginary Unit & Powers of i
• Operations with Complex Numbers
• Quadratic Equations with Complex Solutions
• Conjugates, Modulus & the Complex Plane
• Fundamental Theorem of Algebra & Complete Factorization

How to support without taking over

• Ask the learner to define inputs, outputs, units, and domain.
• Ask which property or theorem justifies each transformation.
• Request an independent check by substitution, graph, table, or alternate method.
• Encourage correction notes rather than erasing evidence of learning.
• Use the calculator after the mathematical setup is visible.

Evidence to preserve

Keep one worked example, one correction, one application or project artifact, the mastery result, and a reflection explaining growth and next steps.

Applied investigation

Polynomial Structure & Complex-Zero Investigation asks the learner to define a real question, construct mathematics, validate results, state uncertainty, and communicate a defensible conclusion.