11 x1 t01 03 factorising (2014)

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11 x1 t01 03 factorising (2014)

  1. 1. Factorising
  2. 2. Factorising 1) Look for a common factor
  3. 3. Factorising 1) Look for a common factor 2) (i) 2 terms  difference of two squares
  4. 4. Factorising 1) Look for a common factor 2) (i) 2 terms  difference of two squares  sum/difference of two cubes
  5. 5. Factorising 1) Look for a common factor 2) (i) 2 terms  difference of two squares  sum/difference of two cubes (ii) 3 terms  quadratic trinomial
  6. 6. Factorising 1) Look for a common factor 2) (i) 2 terms  difference of two squares  sum/difference of two cubes (ii) 3 terms  quadratic trinomial (iii) 4 terms  grouping in pairs
  7. 7. 1. Common Factor factorising = dividing by common factor
  8. 8. 1. Common Factor e.g. (i ) ax  bx factorising = dividing by common factor
  9. 9. 1. Common Factor e.g. (i ) ax  bx  x  a  b  factorising = dividing by common factor
  10. 10. 1. Common Factor e.g. (i ) ax  bx  x  a  b  (ii ) 5 x 2  10 x factorising = dividing by common factor
  11. 11. 1. Common Factor e.g. (i ) ax  bx  x  a  b  (ii ) 5 x 2  10 x  5 x  x  2  factorising = dividing by common factor
  12. 12. 1. Common Factor e.g. (i ) ax  bx  x  a  b  (ii ) 5 x 2  10 x  5 x  x  2  (iii ) mx  nx  my  ny factorising = dividing by common factor
  13. 13. 1. Common Factor e.g. (i ) ax  bx  x  a  b  (ii ) 5 x 2  10 x  5 x  x  2  factorising = dividing by common factor (iii ) mx  nx  my  ny  x  m  n   y  m  n 
  14. 14. 1. Common Factor e.g. (i ) ax  bx  x  a  b  (ii ) 5 x 2  10 x  5 x  x  2  factorising = dividing by common factor (iii ) mx  nx  my  ny  x  m  n   y  m  n    m  n  x  y 
  15. 15. 1. Common Factor e.g. (i ) ax  bx  x  a  b  (ii ) 5 x 2  10 x  5 x  x  2  factorising = 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. 16. 1. Common Factor e.g. (i ) ax  bx  x  a  b  (ii ) 5 x 2  10 x  5 x  x  2  factorising = 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. 17. 1. Common Factor e.g. (i ) ax  bx  x  a  b  (ii ) 5 x 2  10 x  5 x  x  2  factorising = 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. 18. 1. Common Factor e.g. (i ) ax  bx  x  a  b  (ii ) 5 x 2  10 x  5 x  x  2  factorising = 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. 19. 1. Common Factor e.g. (i ) ax  bx  x  a  b  (ii ) 5 x 2  10 x  5 x  x  2  factorising = 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. 20. 1. Common Factor e.g. (i ) ax  bx  x  a  b  (ii ) 5 x 2  10 x  5 x  x  2  factorising = 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. 21. 1. Common Factor e.g. (i ) ax  bx  x  a  b  (ii ) 5 x 2  10 x  5 x  x  2  factorising = 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. 22. 1. Common Factor e.g. (i ) ax  bx  x  a  b  (ii ) 5 x 2  10 x  5 x  x  2  factorising = 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. 23. 1. Common Factor e.g. (i ) ax  bx  x  a  b  (ii ) 5 x 2  10 x  5 x  x  2  factorising = 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. 24. 3. Quadratic Trinomial a) Monic Quadratic  x  a  x  b   x 2   a  b  x  ab
  25. 25. 3. Quadratic Trinomial a) Monic Quadratic  x  a  x  b   x 2   a  b  x  ab e.g. (i ) x 2  9 x  18
  26. 26. 3. Quadratic Trinomial a) Monic Quadratic  x  a  x  b   x 2   a  b  x  ab e.g. (i ) x 2  9 x  18   18 9
  27. 27. 3. Quadratic Trinomial a) Monic Quadratic  x  a  x  b   x 2   a  b  x  ab e.g. (i ) x 2  9 x  18   x  6  x  3   18 9
  28. 28. 3. Quadratic Trinomial a) Monic Quadratic  x  a  x  b   x 2   a  b  x  ab e.g. (i ) x 2  9 x  18   x  6  x  3 (ii ) t 2  4t  3   18 9
  29. 29. 3. Quadratic Trinomial a) Monic Quadratic  x  a  x  b   x 2   a  b  x  ab e.g. (i ) x 2  9 x  18   x  6  x  3 (ii ) t 2  4t  3   18 9 3   4
  30. 30. 3. Quadratic Trinomial a) Monic Quadratic  x  a  x  b   x 2   a  b  x  ab e.g. (i ) x 2  9 x  18   x  6  x  3 (ii ) t 2  4t  3   t  3 t  1   18 9 3   4
  31. 31. 3. Quadratic Trinomial a) Monic Quadratic  x  a  x  b   x 2   a  b  x  ab e.g. (i ) x 2  9 x  18   x  6  x  3 (ii ) t 2  4t  3   t  3 t  1 (iii ) x 2  5 xy  4 y 2   18 9 3   4
  32. 32. 3. Quadratic Trinomial a) Monic Quadratic  x  a  x  b   x 2   a  b  x  ab e.g. (i ) x 2  9 x  18   x  6  x  3 (ii ) t 2  4t  3   t  3 t  1   18 9 3   4 (iii ) x 2  5 xy  4 y 2   4 y 2   5 y
  33. 33. 3. Quadratic Trinomial a) Monic Quadratic  x  a  x  b   x 2   a  b  x  ab e.g. (i ) x 2  9 x  18   x  6  x  3 (ii ) t 2  4t  3   t  3 t  1   18 9 3   4 (iii ) x 2  5 xy  4 y 2   4 y 2   x  y  x  4 y    5 y
  34. 34. b) Splitting the Middle
  35. 35. b) Splitting the Middle e.g. (i ) 3x 2  4 x  7
  36. 36. b) Splitting the Middle e.g. (i ) 3x  4 x  7 2   21 4 Multiply the constant by the coefficient of x squared 7  3
  37. 37. b) Splitting the Middle   21 e.g. (i ) 3x  4 x  7  3x 2  3x  7 x  7   4 2 Multiply the constant by the coefficient of x squared 7  3
  38. 38. b) Splitting the Middle   21 e.g. (i ) 3x  4 x  7  3x 2  3x  7 x  7   4  3 x  x  1  7  x  1 2 Multiply the constant by the coefficient of x squared 7  3
  39. 39. b) Splitting the Middle   21 e.g. (i ) 3x  4 x  7  3x 2  3x  7 x  7   4  3 x  x  1  7  x  1 2   x  1 3 x  7  Multiply the constant by the coefficient of x squared 7  3
  40. 40. b) Splitting the Middle   21 e.g. (i ) 3x  4 x  7  3x 2  3x  7 x  7   4  3 x  x  1  7  x  1 2   x  1 3 x  7  (ii ) 2 x 2  5 x  12 Multiply the constant by the coefficient of x squared 7  3
  41. 41. b) Splitting the Middle   21 e.g. (i ) 3x  4 x  7  3x 2  3x  7 x  7   4  3 x  x  1  7  x  1 2   x  1 3 x  7  (ii ) 2 x 2  5 x  12   24   5 Multiply the constant by the coefficient of x squared 7  3
  42. 42. b) Splitting the Middle   21 e.g. (i ) 3x  4 x  7  3x 2  3x  7 x  7   4  3 x  x  1  7  x  1 2   x  1 3 x  7    24 (ii ) 2 x 2  5 x  12  2 x 2  8 x  3 x  12   5 Multiply the constant by the coefficient of x squared 7  3
  43. 43. b) Splitting the Middle   21 e.g. (i ) 3x  4 x  7  3x 2  3x  7 x  7   4  3 x  x  1  7  x  1 2   x  1 3 x  7    24 (ii ) 2 x 2  5 x  12  2 x 2  8 x  3 x  12   5  2 x  x  4  3 x  4 Multiply the constant by the coefficient of x squared 7  3
  44. 44. b) Splitting the Middle   21 e.g. (i ) 3x  4 x  7  3x 2  3x  7 x  7   4  3 x  x  1  7  x  1 2   x  1 3 x  7    24 (ii ) 2 x 2  5 x  12  2 x 2  8 x  3 x  12   5  2 x  x  4  3 x  4   x  4  2 x  3 Multiply the constant by the coefficient of x squared 7  3
  45. 45. b) Splitting the Middle   21 e.g. (i ) 3x  4 x  7  3x 2  3x  7 x  7   4  3 x  x  1  7  x  1 2 Multiply the constant by the coefficient of x squared 7  3   x  1 3 x  7    24 (ii ) 2 x 2  5 x  12  2 x 2  8 x  3 x  12   5  2 x  x  4  3 x  4   x  4  2 x  3 Exercise 1C; 1e, 2f, 3d, 4ejo, 5adhkn, 6ace etc, 7ace etc, 8*bdfij

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