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Math Help - Algebra HW questions

  1. #1
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    Algebra HW questions

    Hello,

    I am currently taking a college algebra class online and needs some help on a few homework questions. My instructor has not gotten back to me yet, so I found this forum and thought I would see if any of you could get me in the right direction.

    The first problem is dealing with graphing a quadratic function; plus finding the real zeros and minimums for:

    f(x)= (1/2)x^3 - 8x^2 - 3


    The next one is to find all the solutions (real and complexe) for:

    4x^3 - 4x^2 + 3x - 3 = 0


    And, one more using long division: (6x^3 + x^2 - 1) / (x-2)


    If anyone could help me out with these I would appreciate it. I have not had an algebra class for a few years and taking the class in an online format has not been the best experience. Thanks if you can help out.
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  2. #2
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    Quote Originally Posted by RBry View Post
    ...

    The next one is to find all the solutions (real and complexe) for:

    4x^3 - 4x^2 + 3x - 3 = 0


    And, one more using long division: (6x^3 + x^2 - 1) / (x-2)


    ...
    You can factor the LHS of the equation:

    4x^3 - 4x^2 + 3x - 3 = 0~\implies~4x^2(x-1)+3(x-1)=0~\implies~(x-1)(4x^2+3)=0

    I'll leave the rest for you.

    Long division:
    Code:
                                                               51
       (6x^3 +  x^2      -  1)  (x - 2) = 6x^2 + 13x + 26 + ------
      -(6x^3 - 12x^2)                                         x - 2
      --------------------
               13x^2 + 0*x
             -(13x^2 - 26x)
             ----------------
                        26x - 1
                      -(26x - 52)
                       ---------------
                              51
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