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Chatty reference · maths1 week 4

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1 min read
2026-08-16

4. Maths Week 4 — Algebra of Polynomials

Officially this includes polynomial arithmetic, algorithms, polynomial graphs and polynomial creation. citeturn1view0

Concepts

  • Polynomial expressions
  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Polynomial algorithms
  • Roots / xx-intercepts
  • Multiplicity
  • End behaviour
  • Turning points
  • Polynomial graphing
  • Constructing polynomials

Pattern families

Easy
  • Add/subtract polynomials.
  • Multiply.
  • Evaluate polynomial.
  • Identify degree.
  • Identify leading coefficient.
Medium
  • Polynomial division.
  • Factorization.
  • Roots → polynomial.
  • Polynomial → graph characteristics.
Hard
  • Multiplicity + graph behaviour.
  • Determine unknown coefficients from constraints.
  • Reconstruct polynomial from roots/points.
  • Reason about end behaviour without fully expanding.

Important mental model

A polynomial isn't merely:
"some algebraic expression."
Think of it simultaneously as:
expression↔equation↔function↔graph\text{expression} \leftrightarrow \text{equation} \leftrightarrow \text{function} \leftrightarrow \text{graph}
Quiz questions can move between those representations.
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