Quarter 1_Division_of_Polynomials_Grade10.pptx

mathematics 10

1. Division of Polynomials Grade 10 Mathematics Presented by: [Your Name] Date: [Insert Date]

2. Learning Objectives Define and identify polynomials Use long and synthetic division to divide polynomials Apply the Remainder and Factor Theorems Solve real-life problems using polynomial division

3. SOLO Taxonomy Overview Prestructural : Basic recall (terms, symbols) Unistructural: Simple division Multistructural : Use procedures Relational: Apply theorems Extended Abstract: Create and apply

4. What is a Polynomial? - An algebraic expression with variables and coefficients Examples: Monomial: 3x, Binomial: x² - 5, Trinomial: 2x² + 3x - 4 - Terms: degree, leading coefficient, constant

5. Why Divide Polynomials? Simplify expressions Analyze functions Used in real-world and advanced math

6. Long Division Steps 1. Divide leading terms 2. Multiply 3. Subtract 4. Bring down 5. Repeat

7. Long Division Example Divide: (x² + 3x + 2) ÷ (x + 1)

8. Practice: Long Division Try: (2x³ + 5x² - x - 3) ÷ (x + 2) Work with a partner.

9. What is Synthetic Division? Shortcut for divisors of the form (x - a) Coefficient-based method F aster and simpler

10. Synthetic Division Steps 1. Write coefficients 2. Use zero of divisor 3. Bring down first number 4. Multiply and add repeatedly 5. Last number = remainder

11. Synthetic Division Example Divide: x³ - 4x² + x + 6 ÷ (x - 3) [Use synthetic division table]

12. Practice: Synthetic Division Problem: 2x³ - 3x² + 4x - 5 ÷ (x - 2)

13. Remainder Theorem f(a) = remainder of f(x) ÷ (x - a) Example: f(x) = x³ + 2x² - 5x + 1, find f(2)

14. Factor Theorem If f(a) = 0, then x - a is a factor Example: Is x - 1 a factor of x³ - 2x² - x + 2?

15. Common Mistakes - Forgetting to subtract - Using synthetic for non-linear divisors - Not using zero placeholders

16. Mixed Practice Problems 1. (x³ + 2x² - x - 2) ÷ (x + 1) 2. (2x³ + 3x - 5) ÷ (x - 2) 3. Remainder of x³ - x + 1 ÷ (x - 1)

17. Real-Life Application A rectangle has area 2x² + 7x + 3 One side: x + 1 Find the other side using division

18. Summary ✅ Long & Synthetic Division ✅ Remainder Theorem ✅ Factor Theorem ✅ Applications

19. Exit Ticket - One thing I learned today - One question I still have - A polynomial problem I’ll try at home

20. Credits & Resources - Examples from math books - Created by: [Your Name] - Designed for Grade 10