## brodybarnes35 one year ago Which of the following represents the factored form of f(x) = x^3 − 64x? f(x) = x(x + 8)(x − 8) f(x) = (x − 8)(x + 8) f(x) = x(x − 8)^2 f(x) = x(x^2 − 8)

1. brodybarnes35

@Hero

2. brodybarnes35

FAN AND MEDAL

3. brodybarnes35

idk :/ thats embarrassing wow

4. brodybarnes35

but really idk could you explain

5. brodybarnes35

ohhhh im so stupid sorry X

6. brodybarnes35

-64 = x? what

7. brodybarnes35

9 and 7

8. brodybarnes35

no thats 63 my b

9. brodybarnes35

OMG WTH IM DUMB

10. brodybarnes35

8*8 UGHHH

11. brodybarnes35

-8 * 8

12. brodybarnes35

???

13. Hero

@brodybarnes35, what happens to the expression after you factor out the x?

14. brodybarnes35

so its either a or b right

15. brodybarnes35

idk @hero

16. brodybarnes35

a or b right @mehek14 @hero ?

17. brodybarnes35

@Mehek14 ???

18. brodybarnes35

o ok :/

19. brodybarnes35

@Nnesha can you help?

20. Nnesha

first find GCF(greatest common factor ) so there is x common in both terms right ? now take out the x from x^3 and -64x or in other words divide both terms by common factor $\rm x^3-64x=x(???-???)$

21. Nnesha

|dw:1439937064914:dw| divide both terms by common factor and write your answer in the parentheses.

22. brodybarnes35

if you divide by x the outcome would be the same?

23. brodybarnes35

@Nnesha

24. Nnesha

not yet.there is one more step. just divide x^3 by x and then -64x by x

25. Nnesha

x^3/x= ?? -64x/x= ?

26. brodybarnes35

= x^3 =-64x the outcome is the same when you divide...or am i doing it wrong

27. brodybarnes35

wait does the x disappear?

28. Nnesha

i don't get it. what do you mean? x^3 over x isn't equal to x^3

29. Nnesha

x^3 is same as x times x times x $\huge\rm \frac{ x \times x \times x }{ x }$can you divide now?

30. brodybarnes35

its 1x or x?

31. Nnesha

x^3 is same as x times x times x $\huge\rm \frac{ x \times x \times \cancel{x} }{\cancel{ x }}$how many x's wre there ?

32. brodybarnes35

2x? now

33. Nnesha

x^3 is same as x times x times x $\huge\rm \frac{\color{Red}{ x} \times\color{Red}{ x} \times \cancel{\color{Red}{x}} }{\cancel{ x }}$how many x's wre there ?

34. brodybarnes35

2x

35. Nnesha

no when you multiply same bases you should add their exponents $\huge\rm x^m \times x^n = x^{m+n}$ when you ADD same bases then you should add their coefficient 1x+1x=(1+1))x=2x

36. Nnesha

and x is same as x to the one power $\rm x^1 \times x^1 =x^{??}$

37. brodybarnes35

x^2

38. Nnesha

right so x^3 over x = x^2|dw:1439937679559:dw| now divide -64x over x ?

39. Hero

Another way to understand factoring is to think of it in terms of the distributive property. ab + ac = a(b + c) In other words, a is common to both terms on the left so we factor it out to get the expression on the right.

40. brodybarnes35

ummm that would be -64x^2?

41. Nnesha

$\frac{ -64x }{ x} = ?$ here you have to divide by x what would get when you divide same bases ? like 2/2 = ?

42. brodybarnes35

2/2 = 1 right so -64x would be -64x?

43. Nnesha

you are right. -64x would be -64x but what is $\huge\rm \frac{ -64\color{Red}{x} }{ \color{Red}{x} } = ?$

44. brodybarnes35

x^1????

45. Nnesha

Take out x from -64x. that's it.

46. brodybarnes35

omg wow that was simple -.- im dumb

47. Nnesha

so when you take out x from -64x what will u have left with ?

48. brodybarnes35

-64?

49. Nnesha

right!!

50. brodybarnes35

ok so what happens now lol?

51. Nnesha

|dw:1439938027333:dw| $\huge\rm x(x^2-64)$ now apply the difference of square method $\huge\rm a^2-b^2=(a+b)(a-b)$

52. Nnesha

$\huge\rm x(\color{red}{x^2-64})$ now apply the difference of square method $\huge\rm a^2-b^2=(a+b)(a-b)$ take square of both terms in the parentheses write ur answer as (sqrt of 1st term + sqrt of 2nd term)(sqrt of 1st term - sqrt of 2nd term )

53. brodybarnes35

x^3 - 64x

54. Nnesha

that's the original equation what about it ?

55. brodybarnes35

oh nvm

56. brodybarnes35

what a and what is b

57. Nnesha

a and b are variables a = first term b= 2nd term

58. brodybarnes35

yeah but what are they like number wise..

59. Nnesha

|dw:1439938335253:dw|

60. brodybarnes35

x^2 - 64^2 = ( x2 + 64) ( x2 - 64)?

61. Nnesha

no take square root of both terms look at the equation i gave you it's not $\huge\rm a^2-b^2\cancel{=}(a^2-b^2)(a^2+b^2)$

62. brodybarnes35

B

63. Nnesha

how did you get b? what about common that's outside the parentheses?

64. Nnesha

common factor*

65. brodybarnes35

because just they look alike ( - )( + ) the signs match... am i right

66. Nnesha

|dw:1439938542139:dw| take square root of both terms write your answer in the parentheses

67. brodybarnes35

it is B!!

68. anonymous

its A x(x-8)(x+8)

69. Nnesha

don't look at the answer choices

70. brodybarnes35

oh its a yikes

71. Nnesha

why it's a ?

72. brodybarnes35

she said it

73. Nnesha

she is not gonna be there when you have to take final exam.

74. brodybarnes35

(x - 8)(x + 8) right?

75. anonymous

x(x^2-64)= x^3-64x

76. Nnesha

that should go in the parentheses|dw:1439938908541:dw| common should stay there outside the parentheses.

77. brodybarnes35

ohhhh so A

78. brodybarnes35

@Nnesha

79. anonymous

yes

80. Nnesha

yes|dw:1439938990977:dw|

81. brodybarnes35

ok thanks can you help with one more?

82. brodybarnes35

83. brodybarnes35

???

84. Nnesha

@ana123456 don't give out direct answer especially when someone spnd one HOUR to teach.

85. Nnesha

and sorry i have to go :) good luck!!

86. brodybarnes35

ok

87. brodybarnes35

ana can you help lol

88. brodybarnes35

@ana123456

89. brodybarnes35

one more question pls

90. anonymous

sure

91. brodybarnes35

nvm i got it thanks

92. anonymous

you're welcome