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MATH TIME!

Discussion in 'User Topics' started by Mr.Lame, Jan 9, 2018.

  1. Mr.Lame

    Mr.Lame Regular

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    My brains dead i feel it, talk to you tomorrow , Thanks again Mark I super appreciate your help.
     
  2. Mr.Lame

    Mr.Lame Regular

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    Markkkkyyy poo @MarkFL .


    Factor over the integers the polynomial that is quadratic in form. (Factor your answer completely.)
    x^4 − 13x^2 + 36

    Last question T.T
     
  3. mikeconley11

    mikeconley11 Addict Pic Mod

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    I think you should start paying him
     
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  4. Mr.Lame

    Mr.Lame Regular

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    I pay in respect
     
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  5. MarkFL

    MarkFL La Villa Strangiato Staff Member Mod Squad

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    Okay, first we observe that this is a quadratic in x^2.

    So, we want to look for two factors of 36 whose sum is -13, and they are -4 and -9...so we have:

    x^4 - 13x^2 + 36 = (x^2 - 4)(x^2 - 9)

    Now, we see both factors are differences of squares, so we have:

    x^4 - 13x^2 + 36 = (x^2 - 4)(x^2 - 9) = (x^2 - 2^2)(x^2 - 3^2) = (x + 2)(x - 2)(x + 3)(x - 3)

    And we're done. :)
     
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  6. Mr.Lame

    Mr.Lame Regular

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    How the fuck did you do that so fast . You rock for real though :bdate:
     
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  7. Mr.Lame

    Mr.Lame Regular

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    @MarkFL can you just be my tutor? Hahahaha
     
  8. MarkFL

    MarkFL La Villa Strangiato Staff Member Mod Squad

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    Please feel free to ask any questions here, even questions about concepts and not just actual assigned problems. I will do my best to explain. :)
     
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  9. Mr.Lame

    Mr.Lame Regular

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    I'm going to need this more than you'd ever know!
     
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  10. Mr.Lame

    Mr.Lame Regular

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    Hey @MarkFL I do not understand how to do this question.
     
  11. Mr.Lame

    Mr.Lame Regular

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    List the four smallest elements of the set.
    {y|y = x2 − 7, x [​IMG] integers}
     
  12. Mr.Lame

    Mr.Lame Regular

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  13. MarkFL

    MarkFL La Villa Strangiato Staff Member Mod Squad

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    What's the question?
     
  14. MarkFL

    MarkFL La Villa Strangiato Staff Member Mod Squad

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    Nevermind...you posted it...
     
  15. MarkFL

    MarkFL La Villa Strangiato Staff Member Mod Squad

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    What is the smallest x^2 can be?
     
  16. Mr.Lame

    Mr.Lame Regular

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    Infinity? D:
     
  17. MarkFL

    MarkFL La Villa Strangiato Staff Member Mod Squad

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    That's the largest value it can approach as x gets farther and farther from zero. The smallest value x^2 can be is zero, and that's when x is zero. So, given the smallest value for x^2 is zero, then the smallest value for y will be -7 because y is defined to be x^2 - 7. And so given that y(x) = x^2 - 7, we have:

    y(0) = 0^2 - 7 = -7

    Next we observe that if we move one unit away from zero, to ±1, we find:

    y(±1) = (±1)^2 - 7 = 1 - 7 = -6

    Likewise:

    y(±2) = (±2)^2 - 7 = 4 - 7 = -3

    y(±3) = (±3)^2 - 7 = 9 - 7 = 2

    And so the 4 smallest elements of the given set are {-7, -6, -3, 2}. :)
     
  18. Mr.Lame

    Mr.Lame Regular

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    You lost me T.T
     
  19. MarkFL

    MarkFL La Villa Strangiato Staff Member Mod Squad

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    Are you familiar with parabolic curves, specifically the vertex and axis of symmetry?
     
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  20. Mr.Lame

    Mr.Lame Regular

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    Not really, most of this stuff I forgot since pre calc 11 two years ago.
     

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