Lesson Plan

• Identify linear and quadratic factors of a polynomial.
• Apply the Factor Theorem and synthetic division to locate linear factors.
• Factorise a cubic polynomial into a linear factor and a quadratic factor.
• Simplify the resulting quadratic factor using standard techniques.

• Projector or interactive whiteboard
• Printed worksheet with practice problems
• Calculator for checking roots
• Algebra tiles (optional)
• Whiteboard markers and erasers
• Synthetic division handout

Begin with a quick mental‑math challenge: “If P(2)=0, what does that tell us about P(x)?” Connect this to students’ prior work on the Factor Theorem. Explain that today they will learn a systematic way to break any cubic into a linear factor and a quadratic factor, and they will be able to check their work using synthetic division.

1. Do‑Now (5′): Students complete a short quiz on identifying factors of simple polynomials.
2. Mini‑lecture (10′): Review the Factor Theorem and introduce the Rational Root Test with examples on the board.
3. Guided Practice (12′): Work through the example P(x)=2x³‑3x²‑8x+12, demonstrating synthetic division step‑by‑step.
4. Collaborative Activity (15′): In pairs, students use the handout to test candidates, perform synthetic division, and factor the resulting quadratic for a new cubic.
5. Checking Understanding (5′): Whole‑class “exit slip” where each group writes the linear factor they found and the quadratic remainder.
6. Extension (Optional, 5′): Introduce grouping method for cubics that lend themselves to it.

Recap the decision flow: test rational roots → apply Factor Theorem → use synthetic division → factor the quadratic. Collect exit slips as a quick assessment and assign three practice problems from the worksheet for homework, encouraging students to show all steps.