Day4_Factor_Theorem_Lesson_Presentation.pptx

Factor_Theorem_Lesson

1. MATATAG LESSON PLAN – DAY 4 Grade 10 | Mathematics | July 31, 2025

2. I. OBJECTIVES Content Standard: • Demonstrates understanding of key concepts of sequences, polynomials, and polynomial equations. Performance Standard: • Formulates and solves problems involving sequences, polynomials, and polynomial equations in real-life contexts. Learning Competency: • Performs division of polynomials using long division and synthetic division. (M10AL-Ig-1) Objectives: • Knowledge: State and explain the Factor Theorem. • Skills: Use the Factor Theorem to determine if a binomial is a factor. • Attitudes: Appreciate algebraic reasoning and computation.

3. II. CONTENT / III. LEARNING RESOURCES Content Topic: • Using the Factor Theorem to determine if a binomial is a factor of a polynomial. Learning Resources: • K to 12 Math Curriculum Guide • Grade 10 LM (Week 6, Day 4) • DepEd Commons • PowerPoint, charts, graphs

4. IV-A. Reviewing Previous Lesson • Review: What is the Remainder Theorem? • Ask: What does it mean if P(x) ÷ (x - c) leaves 0 remainder?

5. IV-B. Motivation • Ask: Can we tell if something is a factor without full factoring? • Introduce the Factor Theorem.

6. IV-C. Presenting Examples • Explain: If P(c) = 0, then (x - c) is a factor. • Example: P(x) = x³ - x² - 4x + 4; check if x - 2 is a factor.

7. IV-D & E. Practicing Skills • Evaluate P(2); P(2) = 0 → x - 2 is a factor. • Try: P(x) = x³ + x² + x + 2; Check if x + 1 is a factor (P(-1)).

8. IV-F. Developing Mastery Determine if the following are factors: 1. x – 2 ; 4x³ – 3x² - 8x + 4 2. x + 3 ; 2x³ + x² – 13x + 6

9. IV-G. Applications in Daily Living • Simplify formulas in real-life settings. • Used in engineering, coding, computations, and data analysis.

10. IV-H. Generalization • If P(c) = 0, then x - c is a factor of P(x). • This is the Factor Theorem.

11. IV-I. Evaluating Learning Use Factor Theorem to determine if the first is a factor of the second: 1. y + 2 ; 3y⁴ – 6y³ – 5y + 10 2. x – 1 ; x³ – 2x² + x – 2

12. IV-J. Remediation and Enrichment Remediation: • Reinforce evaluating P(x) for various values of x. Enrichment: • Use graphing software or sketch graphs of P(x). • Check if graph crosses x-axis at x = c.