1. 6.1 - Polynomials

2. Monomial

3. Monomial – 1 term

4. Monomial – 1 term; a variable

5. Monomial – 1 term; a variable, number times a variable

6. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables.

7. Operations with Monomials:

8. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3

9. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3

10. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 x·x·x·x

11. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 x·x·x·x

12. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 x·x·x·x·x·x·x

13. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 x·x·x·x·x·x·x

14. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 x·x·x·x·x·x·x x 7

15. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 x·x·x·x·x·x·x x 7 Ex. 2 Simplify x 5 x 3

16. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 x·x·x·x·x·x·x x 7 Ex. 2 Simplify x 5 x 3

17. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 x·x·x·x·x·x·x x 7 Ex. 2 Simplify x 5 x 3 x·x·x·x·x

18. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 x·x·x·x·x·x·x x 7 Ex. 2 Simplify x 5 x 3 x·x·x·x·x

19. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 x·x·x·x·x·x·x x 7 Ex. 2 Simplify x 5 x 3 x·x·x·x·x x·x·x

20. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 x·x·x·x·x·x·x x 7 Ex. 2 Simplify x 5 x 3 x·x·x·x·x x·x·x x 2

21. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 OR x 4 ·x 3 x·x·x·x·x·x·x x 7 Ex. 2 Simplify x 5 x 3 x·x·x·x·x x·x·x x 2

22. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 OR x 4 ·x 3 x·x·x·x·x·x·x x 4+3 x 7 Ex. 2 Simplify x 5 x 3 x·x·x·x·x x·x·x x 2

23. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 OR x 4 ·x 3 x·x·x·x·x·x·x x 4+3 x 7 Ex. 2 Simplify x 5 x 3 x·x·x·x·x x·x·x x 2

24. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 OR x 4 ·x 3 x·x·x·x·x·x·x x 4+3 x 7 Ex. 2 Simplify x 5 x 5 x 3 x 3 x·x·x·x·x x·x·x x 2

25. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 OR x 4 ·x 3 x·x·x·x·x·x·x x 4+3 x 7 Ex. 2 Simplify x 5 x 5 x 3 x 3 x·x·x·x·xx 5-3 x·x·x x 2

26. Monomial – 1 term; a variable, number times a variable, or multiple of numbers and variables. Operations with Monomials: Ex. 1 Simplify x 4 ·x 3 OR x 4 ·x 3 x·x·x·x·x·x·x x 4+3 x 7 Ex. 2 Simplify x 5 x 5 x 3 x 3 x·x·x·x·xx 5-3 x·x·x x 2 x 2

27. Ex. 3 Simplify (y 6 ) 3

29. (y 6 )(y 6 )(y 6 )

30. Ex. 3 Simplify (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6+6+6

31. Ex. 3 Simplify (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6+6+6 y 18

32. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6+6+6 y 18

33. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18

34. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18 y 18

35. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18 y 18 Ex. 4 Simplify (7x 3 y -5 )(4xy 3 )

36. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18 y 18 Ex. 4 Simplify (7x 3 y -5 )(4xy 3 )

37. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18 y 18 Ex. 4 Simplify (7x 3 y -5 )(4xy 3 ) (7·4)

38. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18 y 18 Ex. 4 Simplify (7x 3 y -5 )(4xy 3 ) (7·4)

39. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18 y 18 Ex. 4 Simplify (7x 3 y -5 )(4xy 3 ) (7·4)(x 3 ·x)

40. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18 y 18 Ex. 4 Simplify (7x 3 y -5 )(4xy 3 ) (7·4)(x 3 ·x)

41. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18 y 18 Ex. 4 Simplify (7x 3 y -5 )(4xy 3 ) (7·4)(x 3 ·x)(y 3 ·y -5 )

42. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18 y 18 Ex. 4 Simplify (7x 3 y -5 )(4xy 3 ) (7·4)(x 3 ·x)(y 3 ·y -5 ) 28x 4 y -2

43. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18 y 18 Ex. 4 Simplify (7x 3 y -5 )(4xy 3 ) (7·4)(x 3 ·x)(y 3 ·y -5 ) 28x 4 y -2 28x 4 y 2

44. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18 y 18 Ex. 4 Simplify (7x 3 y -5 )(4xy 3 ) (7·4)(x 3 ·x)(y 3 ·y -5 ) 28x 4 y -2 28x 4 y 2 Ex. 5 Simplify -5x 3 y 3 z 4 20x 3 y 7 z 4

45. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18 y 18 Ex. 4 Simplify (7x 3 y -5 )(4xy 3 ) (7·4)(x 3 ·x)(y 3 ·y -5 ) 28x 4 y -2 28x 4 y 2 Ex. 5 Simplify -5x 3 y 3 z 4 20x 3 y 7 z 4 -5 · x 3-3 · y 3-7 · z 4-4 20

46. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18 y 18 Ex. 4 Simplify (7x 3 y -5 )(4xy 3 ) (7·4)(x 3 ·x)(y 3 ·y -5 ) 28x 4 y -2 28x 4 y 2 Ex. 5 Simplify -5x 3 y 3 z 4 20x 3 y 7 z 4 -5 · x 3-3 · y 3-7 · z 4-4 20 -¼·x 0 ·y -4 ·z 0

47. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18 y 18 Ex. 4 Simplify (7x 3 y -5 )(4xy 3 ) (7·4)(x 3 ·x)(y 3 ·y -5 ) 28x 4 y -2 28x 4 y 2 Ex. 5 Simplify -5x 3 y 3 z 4 20x 3 y 7 z 4 -5 · x 3-3 · y 3-7 · z 4-4 20 -¼·x 0 ·y -4 ·z 0 -¼·1·y -4 ·1

48. Ex. 3 Simplify (y 6 ) 3 OR (y 6 ) 3 (y 6 )(y 6 )(y 6 ) y 6·3 y 6+6+6 y 18 y 18 Ex. 4 Simplify (7x 3 y -5 )(4xy 3 ) (7·4)(x 3 ·x)(y 3 ·y -5 ) 28x 4 y -2 28x 4 y 2 Ex. 5 Simplify -5x 3 y 3 z 4 20x 3 y 7 z 4 -5 · x 3-3 · y 3-7 · z 4-4 20 -¼·x 0 ·y -4 ·z 0 -¼·1·y -4 ·1 4y 4

49. Polynomials

50. Polynomials – Expressions with more than 1 term.

51. Degree

52. Polynomials – Expressions with more than 1 term. Degree – highest combination of exponents on single term.

53. Polynomials – Expressions with more than 1 term. Degree – highest combination of exponents on single term. Ex. 1 Determine the degree of the polynomial.

54. Polynomials – Expressions with more than 1 term. Degree – highest combination of exponents on single term. Ex. 1 Determine the degree of the polynomial. x 3 y 5 – 9x 4

55. Polynomials – Expressions with more than 1 term. Degree – highest combination of exponents on single term. Ex. 1 Determine the degree of the polynomial. x 3 y 5 – 9x 4

56. Polynomials – Expressions with more than 1 term. Degree – highest combination of exponents on single term. Ex. 1 Determine the degree of the polynomial. x 3 y 5 – 9x 4 degree = 8

57. Operations with Polynomials:

58. Operations with Polynomials: Ex. 1 Simplify (5y + 3y 2 ) + (-8y - 6y 2 )

59. Operations with Polynomials: Ex. 1 Simplify (5y + 3y 2 ) + (-8y - 6y 2 ) 5y - 8y + 3y 2 - 6y 2

60. Operations with Polynomials: Ex. 1 Simplify (5y + 3y 2 ) + (-8y - 6y 2 ) 5y - 8y + 3y 2 - 6y 2 -3y - 3y 2

61. Operations with Polynomials: Ex. 1 Simplify (5y + 3y 2 ) + (-8y - 6y 2 ) 5y - 8y + 3y 2 - 6y 2 -3y - 3y 2 Ex. 2 Simplify (9r 2 + 6r + 16) – (8r 2 – 7r + 10)

62. Operations with Polynomials: Ex. 1 Simplify (5y + 3y 2 ) + (-8y - 6y 2 ) 5y - 8y + 3y 2 - 6y 2 -3y - 3y 2 Ex. 2 Simplify (9r 2 + 6r + 16) – (8r 2 – 7r + 10) (9r 2 + 6r + 16) + (-8r 2 + 7r – 10)

63. Operations with Polynomials: Ex. 1 Simplify (5y + 3y 2 ) + (-8y - 6y 2 ) 5y - 8y + 3y 2 - 6y 2 -3y - 3y 2 Ex. 2 Simplify (9r 2 + 6r + 16) – (8r 2 – 7r + 10) (9r 2 + 6r + 16) + (-8r 2 + 7r – 10) 9r 2 – 8r 2 + 6r + 7r + 16 – 10

64. Operations with Polynomials: Ex. 1 Simplify (5y + 3y 2 ) + (-8y - 6y 2 ) 5y - 8y + 3y 2 - 6y 2 -3y - 3y 2 Ex. 2 Simplify (9r 2 + 6r + 16) – (8r 2 – 7r + 10) (9r 2 + 6r + 16) + (-8r 2 + 7r – 10) 9r 2 – 8r 2 + 6r + 7r + 16 – 10 r 2 + 13r + 6

65. Ex. 3 Simplify 4b(cb – zd)

66. 4b·cb – 4b·zd

67. Ex. 3 Simplify 4b(cb – zd) 4b·cb – 4b·zd 4b 2 c – 4bdz

68. Ex. 3 Simplify 4b(cb – zd) 4b·cb – 4b·zd 4b 2 c – 4bdz Ex. 4 Simplify (3x + 8)(2x + 6)

69. Ex. 3 Simplify 4b(cb – zd) 4b·cb – 4b·zd 4b 2 c – 4bdz Ex. 4 Simplify (3x + 8)(2x + 6) 3x(2x + 6) + 8(2x + 6)

70. Ex. 3 Simplify 4b(cb – zd) 4b·cb – 4b·zd 4b 2 c – 4bdz Ex. 4 Simplify (3x + 8)(2x + 6) 3x(2x + 6) + 8(2x + 6) 3x·2x + 3x·6 + 8·2x + 8·6

71. Ex. 3 Simplify 4b(cb – zd) 4b·cb – 4b·zd 4b 2 c – 4bdz Ex. 4 Simplify (3x + 8)(2x + 6) 3x(2x + 6) + 8(2x + 6) 3x·2x + 3x·6 + 8·2x + 8·6 3·2·x·x + 3·6·x + 8·2·x + 8·6

72. Ex. 3 Simplify 4b(cb – zd) 4b·cb – 4b·zd 4b 2 c – 4bdz Ex. 4 Simplify (3x + 8)(2x + 6) 3x(2x + 6) + 8(2x + 6) 3x·2x + 3x·6 + 8·2x + 8·6 3·2·x·x + 3·6·x + 8·2·x + 8·6 6x 2 + 18x + 16x + 48

73. Ex. 3 Simplify 4b(cb – zd) 4b·cb – 4b·zd 4b 2 c – 4bdz Ex. 4 Simplify (3x + 8)(2x + 6) 3x(2x + 6) + 8(2x + 6) 3x·2x + 3x·6 + 8·2x + 8·6 3·2·x·x + 3·6·x + 8·2·x + 8·6 6x 2 + 18x + 16x + 48 6x 2 + 34x + 48