General-Trinomials for public schoolpptx

Trinomials for grade 7

1. Factoring Method #5 Factoring a trinomial in the form:   where a = 1

2. Factoring a trinomial : 2. Product of first terms of both binomials must equal to first term of the trinomial. 1. Write two sets of parenthesis, ( )( ). These will be the factors of the trinomial.    

3. 3. The product of last terms of both binomials must equal to last term of the trinomial ( c ). 4. Think of the FOIL method of multiplying binomials, the sum of the outer and the inner products must equal the middle term ( bx ). Factoring a trinomial :  

4. x x Factors of +8: 1 & 8 2 & 4 -1 & -8 -2 & -4 2 x + 4 x = 6 x 1 x + 8 x = 9 x O + I = bx ? -2 x - 4 x = -6 x -1 x - 8 x = -9 x + 2 + 4 Example: x 2 + 6x + 8 ( ) ( )

5. NOTE: By commutative property, factors can be interchanged. Hence, the factors of x 2 + 6x + 8 ( x+2 ) ( x+4 ) can also be expressed as ( x+4 ) ( x+2 )

6. = ( x + 2 ) ( x + 4 ) x 2 + 6x + 8 Check your answer by using FOIL (x+2) (x+4) = x 2 + 4x + 2x + 8 F O I L (x+2) (x+4) = x 2 + 6x + 8 

7. Another Example: x 2 + 4x + 3 = ( ) ( ) x x +3 +1  3 1 + 3 + 1

8. Therefore x 2 + 4x + 3 = ( x + 3 ) ( x + 1 ) Check using FOIL

9. Another Example: x 2 + 2x + 1 = ( ) ( ) x x +1 +1 1 1 + 1 + 1

10. Therefore x 2 + 2x + 1 = ( x + 1 ) ( x + 1 ) Check using FOIL

11. Another Example: x 2  x  6 = ( ) ( ) x x +3 2 3 +2  3 + 2 +6 1 6 +1

12. Therefore x 2  x  6 = ( x  3 ) ( x + 2 ) Check using FOIL

13. Another Example: x 2 +2 x  15 = ( ) ( ) x x +5 3 5 +3 + 5  3 +15 1 15 +1

14. Therefore x 2 + 2 x  15 = ( x + 5 ) ( x  3 ) Check using FOIL

15. Try this. x 2 – 4x + 4 ( x – 2 ) ( x – 2 )

16. x 2 – 6x + 8 ( x – 2 ) ( x – 4 )

17. y 2 + 7y + 6 ( y + 6 ) ( y + 1 )

18. y 2 + 7y + 10 ( y + 2 ) ( y + 5 )

19. n 2 + 8n + 15 ( n + 5 ) ( n + 3 )

20. p 2 + 9p + 18 ( p + 3 ) ( p + 6 )

21. r 2 + 2r  15 ( r + 5 ) ( r  3 )

22. x 2 + 3x  18 ( x + 6 ) ( x  3 )

23. x 2 + 4x  21 ( x + 7 ) ( x  3 )

24. x 2 + x  12 ( x + 4 ) ( x  3 )

25. y 2 + 5y  36 ( y + 9 ) ( y  4 )

26. n 2 7n + 12 ( n – 3 ) ( n  4 )

27. x 2 + 3x  6 Not Factorable

28. x 2 + 2x  12 Not Factorable

29. p 2  5p  14 ( p + 2 ) ( p  7 )

30. p 2  14p + 24 ( p  2 ) ( p 12 )

31. a 2 + 6a  27 ( a + 9 ) ( a  3 )

32. a 2 + a  20 ( a + 5 ) ( a  4 )

33. m 2  5m  24 ( m – 8 ) ( m + 3 )

34. m 2  6m  12 Not Factorable

35. 2x 2 + 16x + 30 2 ( x + 3 ) ( x + 5 ) 2 ( x 2 + 8x + 15 )

36. 3x 2  9x  12 3 ( x + 1 ) ( x – 4 ) 3 ( x 2  3x  4 )

37. x 4 + 9x 2  22 ( x 2 + 11 ) ( x 2  2 )

38. x 4 + 3x 2  28 ( x 2 + 7 ) ( x 2  4 ) ( x + 2 )(x  2 ) ( x 2 + 7 )

39. Activity: x 2 + 8x + 7 x 2 + 6x + 9 x 2 + 11x + 30 x 2 – 8x + 15 x 2 – 13x + 36 x 2 + 3x – 10 x 2 + 2x – 48

40. 8. x 2 – x – 20 9. x 2 – 4x – 8 10. y 2 – 6y – 16 11. p 4 + 2p 2 – 63 12. n 4 – 10n 2 – 24 13. 2x 2 + 16x + 30 14. 3x 2 + 3x – 126 15. 4x 4 – 28x 2 – 72

41. Answers

42. Factoring Trinomial such that a  1. You can u se trial and error method!  

43. 2x 2 + 7x + 3 Example: ( ) ( ) 2x x ????! + 3 + 1 +3x +2x +5x ERROR! Try again!

44. 2x 2 + 7x + 3 Example: ( ) ( ) 2x x ????! + 1 + 3 +x +6x +7x Bingo! Nice job!

45. Therefore: The factors of 2x 2 + 7x + 3 are ( 2x + 1 ) ( x + 3 )

46. Check using FOIL ( 2x + 1 ) ( x + 3 ) 2x 2 + 7x + 3

47. 3x 2 + 14 x + 8 Example: ( ) ( ) 3x x ????! + 4 + 2 +4x +6x +10x ERROR! Try again!

48. 3x 2 + 14 x + 8 Example: ( ) ( ) 3x x ????! + 8 + 1 +8x +3x +11x ERROR! Try again!

49. 3x 2 + 14 x + 8 Example: ( ) ( ) 3x x ????! + 2 + 4 +2x +12x +14x Bingo! Nice job!

50. Therefore: The factors of 3x 2 + 14x + 8 are ( 3x + 2 ) ( x + 4 )

51. Check using FOIL ( 3x + 2 ) ( x + 4 ) 3x 2 + 14x + 8

52. 2x 2 + 7 x  4 Example: ( ) ( ) 2x x ????!  2 + 2 2 x +4x +2x ERROR! Try again!

53. 2x 2 + 7 x  4 Example: ( ) ( ) 2x x ????!  4 + 1 4 x +2x 2 x ERROR! Try again!

54. 2x 2 + 7 x  4 Example: ( ) ( ) 2x x ????!  1 + 4  x +8x +7x Bingo! Nice job!

55. Therefore: The factors of 2x 2 + 7x  4 are ( 2x  1 ) ( x + 4 )

56. Check using FOIL ( 2x  1 ) ( x + 4 ) 2x 2 + 7x  4

57. Try this. ( 2x + 5 ) ( x + 1 ) 2x 2 + 7x + 5

58. ( 4x + 3 ) ( x + 2 ) 4x 2 + 11x + 6

59. ( 2x + 3 ) ( 2x + 1 ) 4x 2 + 8x + 3

60. ( 3x + 1 ) ( 2x + 1) 6x 2 + 5x + 1

61. 3 ( 2x 2 + 5x + 2 ) 6x 2 + 15x + 6 3 ( 2x + 1 ) ( x + 2)

62. ( 2x + 1 ) ( x  3 ) 2x 2  5x  3

63. Not factorable 3x 2  8 x  4

64. ( 3x + 4 ) ( x  2 ) 3x 2  2 x  8

65. ( 3x + 4 ) ( 3x  5 ) 9x 2  3 x  20

66. ( 2x + 7 ) ( 4x  3 ) 8x 2 + 22 x  21

67. Quiz/Assignment: Factor the following: 2x 2 + 9x + 7 4x 2 + 12x + 5 3. 2x 2 + 9x + 10 4. 3x 2 + 7x – 8 5. 2x 2 – 7x – 9

68. 6. 4x 2 + 25x + 6 7. 5x 2 + 13x – 6 8. 10x 2 – 31x – 14 9. 4x 2 – 4x – 3 10. 15x 2 + 13x + 2

69. ANSWERS

70. ( 2x + 7 ) ( x + 1 ) ( 2x + 5 ) ( 2x + 1 ) ( 2x + 5 ) ( x + 2 ) Not factorable ( 2x  9) ( x + 1 )

71. 6. ( 4x + 1 ) ( x + 6 ) 7. ( 5x  2 ) ( x + 3 ) 8. ( 5x + 2 ) ( 2x  7) 9. ( 2x + 1 ) ( 2x  3) 10. ( 5x + 1 ) ( 3x + 2)

72. Factoring Technique #5 Factoring By Grouping for polynomials with 4 or more terms