What the learner will study

• Long Division of Polynomials
• Synthetic Division & Efficient Evaluation
• Remainder and Factor Theorems
• Rational Root Theorem & Candidate Zeros
• Solving Higher-Degree Polynomial Equations
• Zeros, Multiplicity & Graph Behavior
• Polynomial Regression, Interpolation & Model Limits

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 Graph Reconstruction & Model Defense asks the learner to define a real question, construct mathematics, validate results, state uncertainty, and communicate a defensible conclusion.