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Math Help - Synthetic Division

  1. #1
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    Synthetic Division

    How do you do synthetic division to find

    (x^2 + 4) Divided By (x-2i)

    and

    f(x)= x^3 -3x^2 +x -3

    zero at x = 3

    I learn by examples, so please show work!
    If you don't want to tell me the answer, just give a example similar to the problems above and the answer and steps to solve the example problem.
    Thank You Very Very much!
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  2. #2
    MHF Contributor
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    Quote Originally Posted by tecktonikk View Post
    How do you do synthetic division to find

    (x^2 + 4) Divided By (x-2i)

    and

    f(x)= x^3 -3x^2 +x -3

    zero at x = 3

    I learn by examples, so please show work!
    If you don't want to tell me the answer, just give a example similar to the problems above and the answer and steps to solve the example problem.
    Thank You Very Very much!
    Note that

    x^2 + 4 = x^2 - (2i)^2 = (x + 2i)(x - 2i)


    So \frac{x^2 + 4}{x - 2i} = \frac{(x + 2i)(x - 2i)}{x - 2i} = x + 2i.
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  3. #3
    Super Member
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    May 2009
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    You can still use synthetic division to divide (x^2 + 4) \div (x-2i):
    Code:
    2i|  1   0   4
    --      2i  -4
       ------------
         1  2i   0
    So the quotient, as Prove It has shown, is x + 2i.

    For the second problem, I'm guessing that you're being asked to show that
    (x^3 -3x^2 +x -3) \div (x - 3) has no remainder. The setup would be like this:
    Code:
    3| 1  -3  1  -3
    --
      --------------
       1
    I'll let you do the rest. If you're stuck, look at this tutorial on synthetic division here: Synthetic Division .


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