Polynomial_Long_Division_Lesson with activity.pptx

Polynomial_Long_Division_Lesson

1. Division of Polynomials Using Long Division

2. Learning Objectives - Define parts of a polynomial division - Describe steps in polynomial long division - Solve polynomial expressions using long division - Show perseverance and logical thinking

3. Quick Review: What are Polynomials? - Terms: Constant, variable, degree, leading coefficient - Sample: x³ - 2x² + 3x + 2 Think-Pair-Share: Can we divide expressions with variables like numbers?

4. Why Learn This? - Where do we divide in real life? - Budgeting, sharing land, dividing items evenly Let’s try: What happens when we divide (x³ - 2x² + 3x + 2) ÷ (x - 1)?

5. Step-by-Step Division Guide 1. Divide first terms 2. Multiply and subtract 3. Bring down next term 4. Repeat until remainder is found

6. Example 1 – Teacher Model Problem: (x³ - 2x² + 3x + 2) ÷ (x - 1) Show each division step-by-step Tip: Align like terms!

7. Try It Together Problem: (x³ - 4x² + x + 6) ÷ (x - 2) Student volunteers do each step

8. One More Practice Problem: (2x² + 9x - 3) ÷ (x + 3) Group work: Solve and compare answers

9. Practice Time! Solve the following: 1. (x³ + x² - x - 1) ÷ (x + 1) 2. (2x³ - 3x² + 4x - 5) ÷ (x - 2) 3. (x² - 6x + 9) ÷ (x - 3) Instruction: Show full solution

10. Where Do We Use Polynomial Division? - Dividing land or inheritance - Budgeting expenses - Predicting stock or inventory Ask: Can you think of another example?

11. What Did We Learn? - Polynomial long division is a step-by-step process - Align like terms - Result is a quotient and sometimes a remainder Ask: What happens if we skip a step?

12. Check Your Understanding Solve: 1. (x³ + 2x² - x - 2) ÷ (x + 1) 2. (3x² + 5x + 2) ÷ (x + 2) 3. (x³ - 1) ÷ (x - 1) Identify quotient and remainder

13. Extra Practice (If Finished Early) Remediation: - (x² + 4x + 3) ÷ (x + 1) - (2x² + 5x + 2) ÷ (x + 2) Enrichment: - (2x⁴ + 3x³ - 5x² + 4x - 6) ÷ (x² + x - 1)

14. Let’s Reflect - How did understanding long division help today? - What part was difficult? What strategy helped? Write/Share: How can this method help in solving real-life problems?