1. Factoring Polynomials Part I.pptx; Mathematics 8
- 1. Quarter 1 MATHEMATICS 8 Mrs. Anne R. Rabino-Mesana
- 2. Factoring Polynomials a. G- Greatest C- Common M- Monomial F- Factor Quarter 1: Lesson 1
- 3. Observe… What is common in the given pictures?
- 4. Observe… What is common in the given pictures?
- 5. What is common in: 2, 4, 6
- 6. Factors of 2, 4 and 6 2- 4- 6- 1, 2 1, 2, 4 1, 2, 3, 6 What is their common factor aside from 1?
- 7. Observe x, 2x, 3x, 4x
- 9. Ways of finding the GCF: Prime Factorization GrEAtEst COMMON FACTOR (GCF) Example: Find the GCF of 8 and 12 8 =2 ∙ 2 ∙ 2 12= 2 ∙ 2 ∙ 3 GCF=
- 10. 1. 16 and 48 Example Find the GCF of: 2. 15 and 21 3. 24 and 36
- 11. What is the GCF of ? GrEAtEst COMMON FACTOR (GCF) Answer: What is the GCF of ? Answer:
- 12. The word “POLYNOMIAL” comes from Latin Greek words: Poly (many) and Nomen (name or term) POLYNOMIAL According to the Compact Oxford English Dictionary
- 13. -An algebraic expression that shows a sum/difference of two or more terms containing whole number exponents on the variable. POLYNOMIAL According to the Compact Oxford English Dictionary
- 14. A variable is a symbol which represents an unknown value. VARIABLE
- 15. A symbol or a number with a fixed value. CONSTANTS
- 16. EXAMPLE OF POLYNOMIAL 𝟒 𝒙 𝟐 − 𝟐 This is a polynomial since the variables have no negative (all positive) exponents.
- 17. EXAMPLE OF POLYNOMIAL 𝟒 𝒙 𝟐 − 𝟐 How many terms do we have? Numerical Coefficient Literal Coefficient Exponent Constant
- 18. GCF: NUMERICAL COEFFICIENTS WITH LITERAL COEFFICIENTS 4 𝑥3 𝑎𝑛𝑑 8 𝑥 2 𝑮𝑪𝑭=𝟐∙𝟐∙ 𝒙∙ 𝒙𝒐𝒓 𝟒 𝒙𝟐 4 𝑥3 =2 ∙ 2 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥 8 𝑥 2 =2 ∙ 2 ∙ 2 ∙ 𝑥 ∙ 𝑥
- 19. 1. Example Find the GCF of: 2. 3.
- 20. Is used to find the Greatest Common Factor of the given pair of monomials. PRIME FACTORIZATION
- 21. 4. Find the GCF 5. 1. 2 𝑎𝑛𝑑 10 3. , 2 . 48 𝑎𝑛𝑑 18
- 23. Example 𝟔 𝒙+ 𝟑 𝒙𝟐 Factor the Polynomial GCMF= GCMF Other Factor 𝟑 𝒙 (𝟐+𝒙) Factored Form
- 24. Example 𝟒 𝒂𝟐 +𝟗 𝒃𝟐 Factor the Polynomial GCMF Other Factor Factored Form
- 25. Example 𝟏𝟐 𝒙𝟑 𝒚𝟓 −𝟐𝟎 𝒙𝟓 𝒚𝟐 𝒛 Factor the Polynomial GCMF Other Factor Factored Form
- 26. Is often called as the reverse process of multiplying polynomials, where we write a polynomial as a product of two or more simpler polynomials FACTORING
- 27. Exercises: 𝟕 𝒑𝟐 − 𝟕 𝒑 Factor the Polynomial GCMF Other Factor Factored Form
- 28. Exercises: 𝟏𝟖 𝒙𝒚 +𝟑 𝒚 Factor the Polynomial GCMF Other Factor Factored Form
- 29. QUIZ: 𝟑 𝒎𝟑 − 𝟖 𝒏𝟐 Factor the Polynomial GCMF Other Factor Factored Form
- 30. QUIZ: 𝟐𝟎 𝒙 𝟓 −𝟑𝟒 𝒙𝟐 Factor the Polynomial GCMF Other Factor Factored Form
- 31. QUIZ: 𝟏𝟓𝒎𝟑 −𝟏𝟓𝒎𝟐 +𝟐𝟎𝒎 Factor the Polynomial GCMF Other Factor Factored Form
- 32. Let us have a great school year together!
- 33. QUIZ: Complete the table Polynomial GCMF Other Factor Factored Form
Editor's Notes
- #3: Answer: Their color is orange What else? (Answers may vary. Some possible answer: All of it are good for our health.)
- #5: All are even numbers and divisible by 2.
- #7: They all have the same variable x.
- #8: Recall: Inductive Reasoning
- #16: Q
- #17: Q
- #19: 2. 1
- #21: 2. 1
- #22: Recall: Inductive Reasoning
- #24: Prime polynomials (factors are 1 and itself)