11X1 T01 03 factorising (2011)

Download 11X1 T01 03 factorising (2011)

Post on 05-Dec-2014

515 views

Category:

Education

1 download

DESCRIPTION

 

TRANSCRIPT

  • 1. Factorising
  • 2. Factorising1) Look for a common factor
  • 3. Factorising1) Look for a common factor2) (i) 2 terms difference of two squares
  • 4. Factorising1) Look for a common factor2) (i) 2 terms difference of two squares sum/difference of two cubes
  • 5. Factorising1) Look for a common factor2) (i) 2 terms difference of two squares sum/difference of two cubes (ii) 3 terms quadratic trinomial
  • 6. Factorising1) Look for a common factor2) (i) 2 terms difference of two squares sum/difference of two cubes (ii) 3 terms quadratic trinomial (iii) 4 terms grouping in pairs
  • 7. 1. Common Factor factorising = dividing by common factor
  • 8. 1. Common Factor factorising e.g. (i ) ax bx = dividing by common factor
  • 9. 1. Common Factor factorising e.g. (i ) ax bx x a b = dividing by common factor
  • 10. 1. Common Factor factorising e.g. (i ) ax bx x a b = (ii ) 5 x 2 10 x dividing by common factor
  • 11. 1. Common Factor factorising e.g. (i ) ax bx x a b = (ii ) 5 x 2 10 x 5 x x 2 dividing by common factor
  • 12. 1. Common Factor factorising e.g. (i ) ax bx x a b = (ii ) 5 x 2 10 x 5 x x 2 dividing by common factor (iii ) mx nx my ny
  • 13. 1. Common Factor factorising e.g. (i ) ax bx x a b = (ii ) 5 x 2 10 x 5 x x 2 dividing by common factor (iii ) mx nx my ny x m n y m n
  • 14. 1. Common Factor factorising e.g. (i ) ax bx x a b = (ii ) 5 x 2 10 x 5 x x 2 dividing by common factor (iii ) mx nx my ny x m n y m n m n x y
  • 15. 1. Common Factor factorising e.g. (i ) ax bx x a b = (ii ) 5 x 2 10 x 5 x x 2 dividing by common factor (iii ) mx nx my ny x m n y m n m n x y 2. Difference of Two Squares a 2 b 2 a b a b
  • 16. 1. Common Factor factorising e.g. (i ) ax bx x a b = (ii ) 5 x 2 10 x 5 x x 2 dividing by common factor (iii ) mx nx my ny x m n y m n m n x y 2. Difference of Two Squares a 2 b 2 a b a b e.g. (i ) 16x 2 1
  • 17. 1. Common Factor factorising e.g. (i ) ax bx x a b = (ii ) 5 x 2 10 x 5 x x 2 dividing by common factor (iii ) mx nx my ny x m n y m n m n x y 2. Difference of Two Squares a 2 b 2 a b a b e.g. (i ) 16x 2 1 = 4 x 1 4 x 1
  • 18. 1. Common Factor factorising e.g. (i ) ax bx x a b = (ii ) 5 x 2 10 x 5 x x 2 dividing by common factor (iii ) mx nx my ny x m n y m n m n x y 2. Difference of Two Squares a 2 b 2 a b a b e.g. (i ) 16x 2 1 = 4 x 1 4 x 1 (ii ) 3 y 2 75
  • 19. 1. Common Factor factorising e.g. (i ) ax bx x a b = (ii ) 5 x 2 10 x 5 x x 2 dividing by common factor (iii ) mx nx my ny x m n y m n m n x y 2. Difference of Two Squares a 2 b 2 a b a b e.g. (i ) 16x 2 1 = 4 x 1 4 x 1 (ii ) 3 y 2 75 =3 y 2 25
  • 20. 1. Common Factor factorising e.g. (i ) ax bx x a b = (ii ) 5 x 2 10 x 5 x x 2 dividing by common factor (iii ) mx nx my ny x m n y m n m n x y 2. Difference of Two Squares a 2 b 2 a b a b e.g. (i ) 16x 2 1 = 4 x 1 4 x 1 (ii ) 3 y 2 75 =3 y 2 25 =3 y 5 y 5
  • 21. 1. Common Factor factorising e.g. (i ) ax bx x a b = (ii ) 5 x 2 10 x 5 x x 2 dividing by common factor (iii ) mx nx my ny x m n y m n m n x y 2. Difference of Two Squares a 2 b 2 a b a b e.g. (i ) 16x 2 1 = 4 x 1 4 x 1 (ii ) 3 y 2 75 =3 y 2 25 =3 y 5 y 5 (iii ) 5 x 5 y x 2 y 2
  • 22. 1. Common Factor factorising e.g. (i ) ax bx x a b = (ii ) 5 x 2 10 x 5 x x 2 dividing by common factor (iii ) mx nx my ny x m n y m n m n x y 2. Difference of Two Squares a 2 b 2 a b a b e.g. (i ) 16x 2 1 = 4 x 1 4 x 1 (ii ) 3 y 2 75 =3 y 2 25 =3 y 5 y 5 (iii ) 5 x 5 y x 2 y 2 =5 x y x y x y
  • 23. 1. Common Factor factorising e.g. (i ) ax bx x a b = (ii ) 5 x 2 10 x 5 x x 2 dividing by common factor (iii ) mx nx my ny x m n y m n m n x y 2. Difference of Two Squares a 2 b 2 a b a b e.g. (i ) 16x 2 1 = 4 x 1 4 x 1 (ii ) 3 y 2 75 =3 y 2 25 =3 y 5 y 5 (iii ) 5 x 5 y x 2 y 2 =5 x y x y x y = x y 5 x y
  • 24. 3. Quadratic Trinomial a) Monic Quadratic x a x b x 2 a b x ab
  • 25. 3. Quadratic Trinomial a) Monic Quadratic x a x b x 2 a b x abe.g. (i ) x 2 9 x 18
  • 26. 3. Quadratic Trinomial a) Monic Quadratic x a x b x 2 a b x abe.g. (i ) x 2 9 x 18 18 9
  • 27. 3. Quadratic Trinomial a) Monic Quadratic x a x b x 2 a b x abe.g. (i ) x 2 9 x 18 18 x 6 x 3 9
  • 28. 3. Quadratic Trinomial a) Monic Quadratic x a x b x 2 a b x abe.g. (i ) x 2 9 x 18 18 x 6 x 3 9 (ii ) t 2 4t 3
  • 29. 3. Quadratic Trinomial a) Monic Quadratic x a x b x 2 a b x abe.g. (i ) x 2 9 x 18 18 x 6 x 3 9 (ii ) t 2 4t 3 3 4
  • 30. 3. Quadratic Trinomial a) Monic Quadratic x a x b x 2 a b x abe.g. (i ) x 2 9 x 18 18 x 6 x 3 9 (ii ) t 2 4t 3 3 t 3 t 1 4
  • 31. 3. Quadratic Trinomial a) Monic Quadratic x a x b x 2 a b x abe.g. (i ) x 2 9 x 18 18 x 6 x 3 9 (ii ) t 2 4t 3 3 t 3 t 1 4 (iii ) x 2 5 xy 4 y 2
  • 32. 3. Quadratic Trinomial a) Monic Quadratic x a x b x 2 a b x abe.g. (i ) x 2 9 x 18 18 x 6 x 3 9 (ii ) t 2 4t 3 3 t 3 t 1 4 (iii ) x 2 5 xy 4 y 2 4 y 2 5 y
  • 33. 3. Quadratic Trinomial a) Monic Quadratic x a x b x 2 a b x abe.g. (i ) x 2 9 x 18 18 x 6 x 3 9 (ii ) t 2 4t 3 3 t 3 t 1 4 (iii ) x 2 5 xy 4 y 2 4 y 2 x y x 4 y 5 y
  • 34. b) Splitting the Middle
  • 35. b) Splitting the Middlee.g. (i ) 3x 2 4 x 7
  • 36. b) Splitting the Middle Multiply the constant by thee.g. (i ) 3x 4 x 7 2 21 coefficient of x squared 4 7 3
  • 37. b) Splitting the Middle Multiply the constant by thee.g. (i ) 3x 4 x 7 2 21 coefficient of x squared 3x 2 3x 7 x 7 4 7 3
  • ...