UNIT OVERVIEW

In this unit, you will learn how to work with third-degree polynomials, also called cubic functions. You already know how to factorise quadratics like $x^2 - 5x + 6$ into $(x-2)(x-3)$. Now you will learn how to factorise expressions like $x^3 - 6x^2 + 11x - 6$.

Two important tools will help you: the Remainder Theorem and the Factor Theorem. These theorems turn a difficult problem into something manageable.

What You Will Learn

• How to identify polynomial functions by their degree
• The Remainder Theorem and how it helps with division
• The Factor Theorem as a tool for finding factors
• Step-by-step methods for factorising cubic polynomials
• How to solve cubic equations using factorisation
• The connection between factors, roots, and graphs

Why This Matters

Engineering: Cubic polynomials model stress distribution in structures. The roots help identify where support is needed.

Business: A profit function might be $P(x) = -x^3 + 12x^2 - 36x + 50$. Finding roots helps determine break-even points.

Packaging design: When cutting squares from sheet material to make boxes, the volume formula becomes a cubic polynomial.

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