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Factoring Techniques: Common Monomial Factor

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FACTORING TECHNIQUES
* Common Monomial Factor (CMF)

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Factoring Techniques: Common Monomial Factor

  1. 1. FACTORING COMMON MONOMIAL FACTOR M R . C A R L O J U S T I N O J . L U N A S e c o n d a r y S c h o o l T e a c h e r I MATHEMATICS 8 Patterns and Algebra (1st Quarter)
  2. 2. The Mathematician’s Prayer Heavenly Father, thank You for the blessings You gave unto us, Add joy to the world, Subtract evil from our lives. Multiply the good things for us. Divide the gifts and share them to others. Convert badness to goodness. Help us raise our needs to You. Extract the roots of immoralities and perform our different functions in life. Tell us all that life is as easy as math. Help us all to solve our problems. This we ask in Jesus’ name, the greatest mathematician who ever lived on earth, Amen.
  3. 3. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA 3 WARM UP Simplify the given expressions.
  4. 4. WARM UP! Simplify the given expressions. 4MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA 𝟑𝒂(𝒂 𝟐 − 𝟕𝒂 + 𝟒) Answer: 𝟑𝒂 𝟑 − 𝟐𝟏𝒂 𝟐 + 𝟏𝟐𝒂
  5. 5. WARM UP! Simplify the given expressions. 5MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA −𝟑𝒂𝒃(𝟔𝒂 𝟐 𝒃 − 𝟐𝒂𝒃 𝟐 ) Answer: −𝟏𝟖𝒂 𝟑 𝒃 𝟐 + 𝟔𝒂 𝟐 𝒃 𝟑
  6. 6. WARM UP! Simplify the given expressions. 6MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA 𝟐𝒙 𝟐 (𝟓𝒙 𝟐 + 𝟒𝒙 − 𝟏) Answer: 𝟏𝟎𝒙 𝟒 + 𝟖𝒙 𝟑 − 𝟐𝒙 𝟐
  7. 7. WARM UP! Simplify the given expressions. 7MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA 𝟒𝒚 𝟑 (𝟐𝒙𝒚 𝟐 + 𝒙𝒚 + 𝟐𝒙) Answer: 𝟖𝒙𝒚 𝟓 + 𝟒𝒙𝒚 𝟒 + 𝟖𝒙𝒚 𝟑
  8. 8. WARM UP! Simplify the given expressions. 8MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA −𝒂𝒃 𝟐 (𝟑𝒂 𝟐 𝒃 − 𝟓𝒂𝒃) Answer: −𝟑𝒂 𝟑 𝒃 𝟑 + 𝟓𝒂 𝟐 𝒃 𝟑
  9. 9. FACTORING COMMON MONOMIAL FACTOR M R . C A R L O J U S T I N O J . L U N A S e c o n d a r y S c h o o l T e a c h e r I MATHEMATICS 8 Patterns and Algebra (1st Quarter)
  10. 10. 10MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA A monomial can be written as a product of its factors. Example: FACTORS 4𝑎2 𝑏5 = 2 ∙ 2 ∙ 𝑎 ∙ 𝑎 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏 8𝑎3 𝑏4 = 2 ∙ 2 ∙ 2 ∙ 𝑎 ∙ 𝑎 ∙ 𝑎 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏 The common factor of 4𝑎2 𝑏5 and 8𝑎3 𝑏4 is 2 ∙ 2 ∙ 𝑎 ∙ 𝑎 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏 = 𝟒𝒂 𝟐 𝒃 𝟒
  11. 11. 11MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA You can also find the greatest common factor of two or more polynomials. Example: GREATESTCOMMON FACTOR 6𝑥2 𝑦 = 2 ∙ 3 ∙ 𝑥 ∙ 𝑥 ∙ 𝑦 9𝑥𝑦 = 3 ∙ 3 ∙ 𝑥 ∙ 𝑦 The GCF of 6𝑥2 𝑦 and 9𝑥𝑦 is 𝟑𝒙𝒚.
  12. 12. 12MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA If the terms of a polynomial have a common factor, the polynomial can be written as a product. This is called factoring. FACTORING
  13. 13. 13MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA Factor 𝟏𝟎𝒎 − 𝟐𝟓𝒏 𝟏𝟎𝒎 = 𝟓 ∙ 𝟐 ∙ 𝒎 𝟐𝟓𝒏 = 𝟓 ∙ 𝟓 ∙ 𝒏 𝑮𝑪𝑭 = 𝟓 𝟏𝟎𝒎 − 𝟐𝟓𝒏 = 𝟓(𝟐𝒎 − 𝟓𝒏)
  14. 14. 14MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA Factor 𝟐𝟏𝒂 𝟐 𝒃 − 𝟑𝟓𝒂𝒃 𝟐 𝟐𝟏𝒂 𝟐 𝒃 = 𝟑 ∙ 𝟕 ∙ 𝒂 ∙ 𝒂 ∙ 𝒃 𝟑𝟓𝒂𝒃 𝟐 = 𝟓 ∙ 𝟕 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃 𝑮𝑪𝑭 = 𝟕 ∙ 𝒂 ∙ 𝒃 𝑮𝑪𝑭 = 𝟕𝒂𝒃
  15. 15. 15MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA Factor 𝟐𝟏𝒂 𝟐 𝒃 − 𝟑𝟓𝒂𝒃 𝟐 𝟐𝟏𝒂 𝟐 𝒃 − 𝟑𝟓𝒂𝒃 𝟐 Answer: 𝟕𝒂𝒃(𝟑𝒂 − 𝟓𝒃)
  16. 16. 16MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA Factor 𝟏𝟔𝒂 𝟐 𝒃 𝟑 − 𝟐𝟎𝒂 𝟑 𝒃 𝟓 𝟏𝟔𝒂 𝟐 𝒃 𝟑 = 𝟐 ∙ 𝟐 ∙ 𝟐 ∙ 𝟐 ∙ 𝒂 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃 𝟐𝟎𝒂 𝟑 𝒃 𝟒 = 𝟐 ∙ 𝟐 ∙ 𝟓 ∙ 𝒂 ∙ 𝒂 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃 𝑮𝑪𝑭 = 𝟐 ∙ 𝟐 ∙ 𝒂 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃 𝑮𝑪𝑭 = 𝟒𝒂 𝟐 𝒃 𝟑
  17. 17. 17MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA Factor 𝟏𝟔𝒂 𝟐 𝒃 𝟑 − 𝟐𝟎𝒂 𝟑 𝒃 𝟓 𝟏𝟔𝒂 𝟐 𝒃 𝟑 − 𝟐𝟎𝒂 𝟑 𝒃 𝟓 Answer: 𝟒𝒂 𝟐 𝒃 𝟑 (𝟒 − 𝟓𝒂𝒃 𝟐 )
  18. 18. 18MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA Factor 𝟐𝟖𝒂 𝟑 𝒃 𝟓 + 𝟑𝟓𝒂 𝟐 𝒃 𝟒 − 𝟏𝟒𝒂𝒃 𝟑 𝟐𝟖𝒂 𝟑 𝒃 𝟓 = 𝟐 ∙ 𝟐 ∙ 𝟕 ∙ 𝒂 ∙ 𝒂 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃 𝟑𝟓𝒂 𝟐 𝒃 𝟒 = 𝟓 ∙ 𝟕 ∙ 𝒂 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃 𝑮𝑪𝑭 = 𝟕 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃 𝑮𝑪𝑭 = 𝟕𝒂𝒃 𝟑 𝟏𝟒𝒂𝒃 𝟑 = 𝟐 ∙ 𝟕 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃
  19. 19. 19MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA Factor 𝟐𝟖𝒂 𝟑 𝒃 𝟓 + 𝟑𝟓𝒂 𝟐 𝒃 𝟒 − 𝟏𝟒𝒂𝒃 𝟑 𝟐𝟖𝒂 𝟑 𝒃 𝟓 + 𝟑𝟓𝒂 𝟐 𝒃 𝟒 − 𝟏𝟒𝒂𝒃 𝟑 Answer: 𝟕𝒂𝒃 𝟑 (𝟒𝒂 𝟐 𝒃 𝟐 + 𝟓𝒂𝒃 − 𝟐)
  20. 20. 20MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA YOU TRY! Find the factors of the given expressions.
  21. 21. 21MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA = 2𝑎 2𝑏 − 5𝑐 EXERCISES 1. 4𝑎𝑏 − 10𝑎𝑐 2. 10𝑎2 + 15𝑎3 3. 16𝑚3 𝑛2 + 20𝑚2 𝑛3 4. 21𝑚𝑛4 − 35𝑚2 𝑛2 + 7𝑚3 𝑛 5. 27𝑥𝑦3 + 81𝑥2 𝑦 − 36𝑥𝑦 = 5𝑎2 2 + 3𝑎 = 4𝑚2 𝑛2 4𝑚 + 5𝑛 = 7𝑚𝑛 3𝑛3 − 5𝑚𝑛 + 𝑚2 = 9𝑥𝑦 3𝑦2 + 9𝑥 − 4
  22. 22. THANK YOU! 22 MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA M R . C A R L O J U S T I N O J . L U N A S e c o n d a r y S c h o o l T e a c h e r I MATHEMATICS 8 Patterns and Algebra (1st Quarter)

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