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Inopeki Group Title

TuringTest, want to continue?

  • 2 years ago
  • 2 years ago

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  1. TuringTest Group Title
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    lol I like the attitude, I better eat though, give me a bit what time is it where you are?

    • 2 years ago
  2. Inopeki Group Title
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    9:45 pm, you? Then go eat :)

    • 2 years ago
  3. TuringTest Group Title
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    alright, just so you know it's easy to send messages via fan message now, so use that instead of a question to hail me

    • 2 years ago
  4. Inopeki Group Title
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    Oh, ill use that!

    • 2 years ago
  5. TuringTest Group Title
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    see you in a bit

    • 2 years ago
  6. Inopeki Group Title
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    Alright

    • 2 years ago
  7. No-data Group Title
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    How do you use those fan messages Turing?

    • 2 years ago
  8. Inopeki Group Title
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    Go to the profile and click "write a fan message"

    • 2 years ago
  9. TuringTest Group Title
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    factor 21x^2+14x

    • 2 years ago
  10. Inopeki Group Title
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    GCF of 21 and 14=7 GCF of x and x^2 is x 21x^2/7x+14x/7x=x(3x+2)?

    • 2 years ago
  11. TuringTest Group Title
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    almost but 1)be careful of notation 21x^2/7x+14x/7x is not equal x(3x+2) 2) remember to keep the whole GCF outside the parentheses

    • 2 years ago
  12. Inopeki Group Title
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    But i thought that if the 7 was on the LHS then it couldnt be on the RHS?

    • 2 years ago
  13. Inopeki Group Title
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    21x^2/7x+14x/7x=7x(3x+2)?

    • 2 years ago
  14. TuringTest Group Title
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    but they are not equal 21x^2/7x+14x/7x=3x+2 not 7x(3x+2) so you must write 21x^2+14x=7x(21x^2/7x+14x/7x)=?

    • 2 years ago
  15. Inopeki Group Title
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    I dont know...

    • 2 years ago
  16. Inopeki Group Title
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    7(3x^2+2)?

    • 2 years ago
  17. TuringTest Group Title
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    you almost have it but you need to put the GCF outside the parentheses what is the GCF?

    • 2 years ago
  18. Inopeki Group Title
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    7x

    • 2 years ago
  19. TuringTest Group Title
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    so that's what goes outside the parentheses

    • 2 years ago
  20. Inopeki Group Title
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    7x(3x^2+2) Cant be right.

    • 2 years ago
  21. TuringTest Group Title
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    what is 21x^2/7x=? rewrite it in a way more comfortable to you if it looks strange

    • 2 years ago
  22. Inopeki Group Title
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    21/7 * x^2/x?

    • 2 years ago
  23. TuringTest Group Title
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    yes...

    • 2 years ago
  24. Inopeki Group Title
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    Im pretty sure thats 3x man

    • 2 years ago
  25. TuringTest Group Title
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    it is, so why did you write 3x^2 above?

    • 2 years ago
  26. Inopeki Group Title
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    Cause you said the other one wasnt right :/ What is the correct way to write it?

    • 2 years ago
  27. TuringTest Group Title
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    here was your first answer x(3x+2) here was the next 21x^2/7x+14x/7x=7x(3x+2) the answer here is correct, I just pointed out that the two expressions above are not equal, I think that may have confused you. next you wrote 7x(3x^2+2) so I think we started to get off track... the answer is 21x^2+14x=7x(3x+2) I just made a point about how you show your work, and what it means.

    • 2 years ago
  28. Inopeki Group Title
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    Ohhhhh :)

    • 2 years ago
  29. TuringTest Group Title
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    write out the process as 21x^2+14x=7x(3x)+7x(2)=7x(3x+2) that is really the best way to show factoring

    • 2 years ago
  30. Inopeki Group Title
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    Oh ok :D Another one?

    • 2 years ago
  31. TuringTest Group Title
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    factor 3t^3+9t^2

    • 2 years ago
  32. TuringTest Group Title
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    sorry, so you know how to divide t^3/t^2 ???

    • 2 years ago
  33. Inopeki Group Title
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    x*x*x ----- right? It should jjust become x? x*x

    • 2 years ago
  34. Inopeki Group Title
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    t, sorry

    • 2 years ago
  35. TuringTest Group Title
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    you got it, so my question stands: factor 3t^3+9t^2

    • 2 years ago
  36. Inopeki Group Title
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    GCF of 3 and 9 is 3. GCF of t^2 and t^3 is t. 3t^3+9t^2=3t(3t^3/3t)+3t(9t^2/3t)=3t(t^3+3t^2)?

    • 2 years ago
  37. TuringTest Group Title
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    check your answer and distribute to see if you get the original: \[3t(t^3+3t^2)=3t(t^3)+3t(3t^2)=3t^4+9t^3\neq3t^3+9t^2\]you didn't divide the terms in the middle right ...but I think more importantly the GCF of t^3 and t^2 is t^2, not t that is because each term can be evenly divided by t^2.

    • 2 years ago
  38. Inopeki Group Title
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    Hm

    • 2 years ago
  39. Inopeki Group Title
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    Oh right!

    • 2 years ago
  40. TuringTest Group Title
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    what is the GCF of t^3+t^5+t^7 ??

    • 2 years ago
  41. Inopeki Group Title
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    Something to the power of something doesnt follow the rules of usual numbers, forgot that. It should be t^5

    • 2 years ago
  42. TuringTest Group Title
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    no it's t^3 and it does follow the rules of regular numbers if you think about it, otherwise it wouldn't be true! look at 16,32,8 what is their GCF ?

    • 2 years ago
  43. Inopeki Group Title
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    8

    • 2 years ago
  44. TuringTest Group Title
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    now rewrite those three numbers as powers of 2

    • 2 years ago
  45. TuringTest Group Title
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    can you do that?

    • 2 years ago
  46. Inopeki Group Title
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    256,1024,64

    • 2 years ago
  47. Inopeki Group Title
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    ?

    • 2 years ago
  48. TuringTest Group Title
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    no I meant like 8=2^3 16=2^? 32=2^?

    • 2 years ago
  49. Inopeki Group Title
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    Oh! 8=2^3 16=2^4 32=2^5

    • 2 years ago
  50. TuringTest Group Title
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    ...and what is their GCF? 2^3 so the GCF of a set of variables is the highest common power to each term -in this case 3 so if we have y^4+y^7+y^9 the GCF is...?

    • 2 years ago
  51. Inopeki Group Title
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    y^4?

    • 2 years ago
  52. TuringTest Group Title
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    right :)

    • 2 years ago
  53. Inopeki Group Title
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    :D

    • 2 years ago
  54. TuringTest Group Title
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    good job :D so now back to our question... factor 3t^3+9t^2 what is the GCF?

    • 2 years ago
  55. Inopeki Group Title
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    3t^2?

    • 2 years ago
  56. TuringTest Group Title
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    right now can you factor it?

    • 2 years ago
  57. Inopeki Group Title
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    3t^3+9t^2=3t^2(3t^3/3t^2)+3t^2(9t^2/3t^2)=3t^2(t+3)?

    • 2 years ago
  58. TuringTest Group Title
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    very nice!!!!!!

    • 2 years ago
  59. Inopeki Group Title
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    I got it!! :D

    • 2 years ago
  60. TuringTest Group Title
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    you totally did :D that is very cool! so now lets see what's so great about factoring say we have f(t)=3t^3+9t^2 and we want to know the 'zeros' of the function that means when the function touches the x-axis, i.e. when f(t)=0 so to answer this we must solve 0=3t^3+9t^2 how can we solve that? by factoring... 0=3t^2(t+3) now you can solve it quickly, any idea which fundamental rule of algebra tells us how?

    • 2 years ago
  61. Inopeki Group Title
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    Nope, sorry

    • 2 years ago
  62. TuringTest Group Title
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    the rule is called the 'zero factor property' it states that if\[ab=0\]then either\[a=0\]or\[b=0\]or both does this rule make logical sense to you?

    • 2 years ago
  63. Inopeki Group Title
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    Yeah

    • 2 years ago
  64. TuringTest Group Title
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    so now look at our factored equation \[0=ab=3t^2(t+3)\]that means that either\[3t^2=0\]or \[t+3=0\]can you solve each of these equations?

    • 2 years ago
  65. TuringTest Group Title
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    *either or both I should say

    • 2 years ago
  66. Inopeki Group Title
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    OH so 3t^2 represents a and t+3 represents b!

    • 2 years ago
  67. TuringTest Group Title
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    exactly that's why i said to learn the rules on this page http://www.capitan.k12.nm.us/teachers/shearerk/basic_rules_of_algebra.htm almost all of algebra is in there, though sometimes it is hidden

    • 2 years ago
  68. Inopeki Group Title
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    3t^2=0 t=0-3t/t t=0-3 t=-3?

    • 2 years ago
  69. TuringTest Group Title
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    no, it's more simple than that, remember the same rule we just used: ab=0 then either a=0 or b=0 or both 3t^2=0 let 3=a t^2=b we know that a=3 cannot be zero, because 3 is never zero, it's a constant that leaves the possibility only of t^2=0 and the number number that times itself is zero is zero so\[3t^2=0\to t=0\]

    • 2 years ago
  70. Inopeki Group Title
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    Ohhhh.. Cause 3x0x0=0?

    • 2 years ago
  71. TuringTest Group Title
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    right so t has to be zero...

    • 2 years ago
  72. Inopeki Group Title
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    Yeah

    • 2 years ago
  73. TuringTest Group Title
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    what about the other possibility t+3=0 ???

    • 2 years ago
  74. Inopeki Group Title
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    How can that be possible when t is 0?

    • 2 years ago
  75. TuringTest Group Title
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    there are two answers to every quadratic equation as you may recall me saying this is cubic so it has 3 actually, we say that zero ocurrs twice in 3t^2=0 because it leads to two 0's as you showed: 3x0x0 we call that a 'multiplicity of 2' so there will be multiple answers, the other is found by solving t+3=0 remember that either a=0 or b=0 or BOTH we don't know so we have to solve them all.

    • 2 years ago
  76. Inopeki Group Title
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    Oh right! This is a quadratic equation. t=-3 on this one so its (0,-3)?

    • 2 years ago
  77. TuringTest Group Title
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    like I said, cubic read what I wrote above please about multiplicity...

    • 2 years ago
  78. Inopeki Group Title
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    Three answers

    • 2 years ago
  79. Inopeki Group Title
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    So these are cubic coordinates?

    • 2 years ago
  80. Inopeki Group Title
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    (0,0,-3)?

    • 2 years ago
  81. TuringTest Group Title
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    not cubic coordinates (I don't know what that is exactly...), it's just that we say that 3t^3+9t^2 has zeros (0,3) - that means the graph of f(x)=3t^3+9t^2 hits zero there... where 0 here has a 'multiplicity' of 2 (that means it occurs twice) and 3 has a multiplicity of 1

    • 2 years ago
  82. Inopeki Group Title
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    So why isnt -3 involved?

    • 2 years ago
  83. TuringTest Group Title
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    sorry typo, meant (0,-3)* and -3 has multiplicity 1*

    • 2 years ago
  84. TuringTest Group Title
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    good catch

    • 2 years ago
  85. Inopeki Group Title
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    Thanks

    • 2 years ago
  86. TuringTest Group Title
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    so do you see what I mean? the zero's of\[f(t)=3t^2+9t^2\]are found by factoring and setting to zero\[0=3t^2(t+3)\]then solving each possibility\[3t^2=0\to t=0\]\[t+3=0\to t=-3\]where we say that for t=0 k=2 and for t=-3 k=1 where k is the multiplicity

    • 2 years ago
  87. Inopeki Group Title
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    Right, the k is cause t is to the power of 3 there.

    • 2 years ago
  88. TuringTest Group Title
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    for the part that had 3t^2=0 we had k=2 (because zero is the answer twice: 3x0x0) for t+3=0 we have k=1 because t is only to the first power and we only have one answer If what you mean is that you noticed that adding up all the k's gave youu 3, the order of the cubic, then you have noticed what is called the Fundamental Theorem of Algebra: "The sum of the multiplicities of the roots of a function is equal to the order of the polynomial" \[k_0+k_{−3}=2+1=3\]

    • 2 years ago
  89. TuringTest Group Title
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    - a very important theorem as the name implies...

    • 2 years ago
  90. Inopeki Group Title
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    I dont really get the theorem, please explain it.

    • 2 years ago
  91. TuringTest Group Title
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    Basically for whatever the highest power variable you have in a polynomial, that is how many answers you have. Note that they may not be all different answers, but the ones that occur more than once are counted as having a higher multiplicity, so if you add up the multiplicities (the k's) that's how many zeros the polynomial has. for example 7x^5+3x^3+2x^2+5x+3=0 must have 5 answers, because it is 5th order x^2+2x+2=0 must have 2 answers, because it is second order

    • 2 years ago
  92. Inopeki Group Title
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    So x^4+5x-4=0 must have 4 answers?

    • 2 years ago
  93. TuringTest Group Title
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    exactly, though it may not be 4 different answers for instance x^4=0 has only the answer x=0, but that zero has a multiplicity of k=4 because 0x0x0x0=0 is how it must be...

    • 2 years ago
  94. Inopeki Group Title
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    Oh, now i get it

    • 2 years ago
  95. TuringTest Group Title
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    good :) do you want to try some more factoring problems? or perhaps you should learn a little about exponents first? or perhaps you are ready top get some rest.... which is it?

    • 2 years ago
  96. Inopeki Group Title
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    I wanna learn something new :D

    • 2 years ago
  97. TuringTest Group Title
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    let's see if this is news to you: simplify\[{x^{14}\over x^{12}}\]

    • 2 years ago
  98. Inopeki Group Title
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    x^2 lol

    • 2 years ago
  99. TuringTest Group Title
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    good that saves a lot of time...

    • 2 years ago
  100. TuringTest Group Title
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    simplify\[\sqrt[3]{x^{21}}\]

    • 2 years ago
  101. Inopeki Group Title
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    x^7?

    • 2 years ago
  102. TuringTest Group Title
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    good :) more time saved...

    • 2 years ago
  103. Inopeki Group Title
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    :D actually i didnt know that

    • 2 years ago
  104. TuringTest Group Title
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    the genereal rule is\[\sqrt[b]{x^{a}}=x^{a/b}\]any radical can be wriitten as a fractional exponent, for instance\[\sqrt x=x^{1/2}\]so... let's try some of that.

    • 2 years ago
  105. Inopeki Group Title
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    Yeah, i assumed that :)

    • 2 years ago
  106. TuringTest Group Title
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    good guess, try to really rationalize it if you can... since you seem to know the rules let's try a trickier one simplify \[\frac{\sqrt[3]{x^2}\sqrt[5]{x^3}}{\sqrt x}\]

    • 2 years ago
  107. Inopeki Group Title
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    x^2/3 * x^3/5 ----------- Its basically this, right? If so, i just need to make the variables "suitable" to x^1/2 be merged, right?

    • 2 years ago
  108. TuringTest Group Title
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    right, just remember that\[x^ax^b=x^{a+b}\]and that\[\frac{x^a}{x^b}=x^{a-b}\]so you're gonna have and subtract to add those fractions, so they all need a common denominator.

    • 2 years ago
  109. TuringTest Group Title
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    so you're gonna have to add and subtract those fractions*

    • 2 years ago
  110. Inopeki Group Title
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    Yeah, thats what i meant by making them suitable to merge

    • 2 years ago
  111. TuringTest Group Title
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    I figured, but that's not a known term to me, just making sure

    • 2 years ago
  112. Inopeki Group Title
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    x^2/3 * x^3/5 x^10/15 * x^9/15 x^19/15 ----------- = =-------------- x^1/2 x^1/2 Now i need to get 19/15 divisible by 2

    • 2 years ago
  113. TuringTest Group Title
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    good so far :)

    • 2 years ago
  114. Inopeki Group Title
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    19/15 ------------38/30

    • 2 years ago
  115. Inopeki Group Title
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    x^38/30 -------- = x^1/2 Actually, dont i need to get them divisible by 15 so i can get 2 as the denominator?

    • 2 years ago
  116. TuringTest Group Title
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    what can you multiply the bottom by to get 1/2 over 30 ?

    • 2 years ago
  117. Inopeki Group Title
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    Oh! x^38/30 -------- = 23/30? No, that cant be it.. x^15/30

    • 2 years ago
  118. TuringTest Group Title
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    yes it can and is but you have to leave the x of course... x^(23/30)

    • 2 years ago
  119. Inopeki Group Title
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    Oh right lol

    • 2 years ago
  120. TuringTest Group Title
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    so that was good, I won't test you on that do you know how to FOIL ?

    • 2 years ago
  121. Inopeki Group Title
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    What?

    • 2 years ago
  122. TuringTest Group Title
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    i.e. simplify (a+b)(c+d)

    • 2 years ago
  123. Inopeki Group Title
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    abcd?

    • 2 years ago
  124. TuringTest Group Title
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    FOIL= First Outer Inner Last|dw:1325979609902:dw|watch the arrows they multiply the first in the brackets, the outer terms, the inner, and the last seperateyl

    • 2 years ago
  125. TuringTest Group Title
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    it's just like distribution, but you have to do a and b seperate

    • 2 years ago
  126. Inopeki Group Title
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    I think i get it. give me another one and ill solve it fast

    • 2 years ago
  127. TuringTest Group Title
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    It's okay if you don't solve it fast actually remember that solving is not simplifying, here we have no = sign so we are simplifying: (x+3)(x+2)

    • 2 years ago
  128. Inopeki Group Title
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    x^2+2x+3x+6?

    • 2 years ago
  129. TuringTest Group Title
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    nice! you can simplify the middle terms

    • 2 years ago
  130. Inopeki Group Title
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    Oh right,x^2+5x+6

    • 2 years ago
  131. TuringTest Group Title
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    nicely done! especially for never having FOILed before. simplify (2x+5)(3x-1)

    • 2 years ago
  132. Inopeki Group Title
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    5x+2x+15x-5?

    • 2 years ago
  133. Inopeki Group Title
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    6x*

    • 2 years ago
  134. TuringTest Group Title
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    careful... what's the first? what's the outer? the others are right.

    • 2 years ago
  135. TuringTest Group Title
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    yes the first is 6x the outer though...

    • 2 years ago
  136. Inopeki Group Title
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    -1?

    • 2 years ago
  137. TuringTest Group Title
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    times what?

    • 2 years ago
  138. Inopeki Group Title
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    2x, maybe thats -2x..

    • 2 years ago
  139. TuringTest Group Title
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    there ya go ;-)

    • 2 years ago
  140. TuringTest Group Title
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    so it should be...?

    • 2 years ago
  141. Inopeki Group Title
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    6x+-2x+15x-5

    • 2 years ago
  142. TuringTest Group Title
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    scratch the extra plus sign, but yes, now simplify...

    • 2 years ago
  143. Inopeki Group Title
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    29x-5?

    • 2 years ago
  144. TuringTest Group Title
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    oh my mistake, you forgot that the first term would be squared First=2x(3x)=6x^2 now what do you get?

    • 2 years ago
  145. Inopeki Group Title
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    6x^2-2x+15x-5?

    • 2 years ago
  146. TuringTest Group Title
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    yes, and now simplify

    • 2 years ago
  147. Inopeki Group Title
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    4x^2+15x-5?

    • 2 years ago
  148. TuringTest Group Title
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    like terms, x with x.... not x with x^2...

    • 2 years ago
  149. Inopeki Group Title
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    so 6x^2+13x-5?

    • 2 years ago
  150. TuringTest Group Title
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    yes. good job. now simplify (2p-3)(5p-1)

    • 2 years ago
  151. Inopeki Group Title
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    10p^2-2p-15p-3? Simplified:10p^2-17p-3

    • 2 years ago
  152. TuringTest Group Title
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    good, but watch the last term negative times negative is...?

    • 2 years ago
  153. Inopeki Group Title
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    Oh right, positive. So 10p^2-17p+3?

    • 2 years ago
  154. Inopeki Group Title
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    2r^2+2r*3t+t*r+3t^2 Simplified: 2r^2+2r^2+3t^2+3t^2

    • 2 years ago
  155. TuringTest Group Title
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    stop before your simplification (which is wrong, sorry) look at the first step: 2r^2+2r*3t+t*r+3t^2 ^^^ should everything be positive?

    • 2 years ago
  156. Inopeki Group Title
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    Oh right.. 2r^2+2r*-3t+t*r

    • 2 years ago
  157. TuringTest Group Title
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    yes but you forgot the last term you should also put parentheses around the negative terms

    • 2 years ago
  158. Inopeki Group Title
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    2r^2+2r*(-3t)+t*(-r)?

    • 2 years ago
  159. TuringTest Group Title
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    lol it got deleted, what was the original problem please?

    • 2 years ago
  160. Inopeki Group Title
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    I cant remember :(

    • 2 years ago
  161. TuringTest Group Title
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    ok another, because we started losing terms in the last one (2y+x)(4y-3x)

    • 2 years ago
  162. Inopeki Group Title
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    8y+2y*3x+x*4y(-3x^2)

    • 2 years ago
  163. TuringTest Group Title
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    there should be four terms what is your first? write out the middle step

    • 2 years ago
  164. TuringTest Group Title
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    it's close in many ways, but there are quite a few mistakes

    • 2 years ago
  165. Inopeki Group Title
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    Ill put them in prenthesis (8y)+(2y*3x)+(x*4y)-(3x^2)

    • 2 years ago
  166. TuringTest Group Title
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    better, but the first is 2y(4y) no? and the outer is a positive times a negative as well

    • 2 years ago
  167. Inopeki Group Title
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    Oh, ill solve this one and then sleep :) (8y^2)+(2y*-3x)+(x*4y)-(3x^2)

    • 2 years ago
  168. TuringTest Group Title
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    nice, so to simplify this first multiply the coefficients...

    • 2 years ago
  169. Inopeki Group Title
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    (8y^2)+(8y^2*-3x^2)-(3x^2)

    • 2 years ago
  170. TuringTest Group Title
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    not I think you're getting tired (8y^2)+(2y*-3x)+(x*4y)-(3x^2)=8y^2-6xy+4xy-3x^2=?

    • 2 years ago
  171. TuringTest Group Title
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    no*

    • 2 years ago
  172. TuringTest Group Title
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    can you simplify the last step?

    • 2 years ago
  173. Inopeki Group Title
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    Yeah, i need to sleep.

    • 2 years ago
  174. TuringTest Group Title
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    for future reference:\[(8y^2)+(2y*-3x)+(x*4y)-(3x^2)\]\[=8y^2-6xy+4xy-3x^2=8y^2-2xy-3y^2\]goodnight!

    • 2 years ago
  175. Inopeki Group Title
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    Good night! Thanks for all youve taught me :D See you tomorrow?

    • 2 years ago
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