Lesson Plan

• Describe the Factor Theorem and Rational Root Theorem as tools for solving cubic equations.
• Apply factor‑by‑grouping, synthetic division, and the Rational Root Test to obtain linear factors of a cubic.
• Reduce a cubic to a quadratic and solve the remaining quadratic by factoring or the quadratic formula.
• Check all obtained solutions by substitution into the original equation.

• Whiteboard and markers
• Projector with slides showing examples
• Student worksheets containing practice cubic equations
• Scientific calculators
• Prepared synthetic‑division handout

Begin with a quick “guess the root” challenge using a simple cubic to spark curiosity. Review the concepts of polynomial degree, factors, and the Factor Theorem that students have already mastered. Explain that today’s success criteria are: correctly identify possible rational roots, factor the cubic, and verify all solutions.

1. Do‑Now (5'): Students list possible rational roots for a given cubic on a sticky note.
2. Mini‑lecture (10'): Review Rational Root Theorem and demonstrate synthetic division on the board.
3. Guided Practice (15'): Work through Example 1 (grouping) together, prompting students to suggest each grouping step.
4. Partner Activity (15'): Students solve Example 2 using the Rational Root Test and synthetic division, checking answers with a calculator.
5. Whole‑class Debrief (10'): Discuss common pitfalls (sign errors, missing negative candidates) and verify solutions.
6. Extension (optional, 5'): Brief introduction to the depressed cubic substitution for advanced learners.
7. Exit Ticket (5'): Each student writes one cubic equation, its possible rational roots, and the first factor they would test.

Recap the step‑by‑step decision flow for solving cubics and emphasize the importance of systematic testing. Collect exit tickets to gauge understanding and assign homework: three new cubic equations to solve using the methods practiced today.