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Math Help - Synthetic substitution regarding cubic

  1. #1
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    Exclamation Synthetic substitution regarding cubic

    I really need help on this!
    It's for Honors Algebra II.

    I need to solve for k.
    The problem is x^3+8x^2+Kx+21; x-6
    The x-6 is the thing that goes in the box, if you know what I'm tAlking about.
    If you could help me, I would really appreciate it.
    Thanks![HTML][/HTML]
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  2. #2
    Member Last_Singularity's Avatar
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    Quote Originally Posted by VictoriaMarie View Post
    I really need help on this!
    It's for Honors Algebra II.

    I need to solve for k.
    The problem is x^3+8x^2+Kx+21; x-6
    The x-6 is the thing that goes in the box, if you know what I'm tAlking about.
    If you could help me, I would really appreciate it.
    Thanks!
    I would help you solve it, except x^3+8x^2+Kx+21 is not an equation. What exactly do you use x-6 for?
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  3. #3
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    Sorry.
    Here's a site that pretty much explains what I'm learning.
    Synthetic Division -- from Wolfram MathWorld
    This I understand, but i have no clue how to solve for that k.
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  4. #4
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    you are looking for the value of k such that (x-6) is a factor of the given cubic.

    Code:
    6]    1        8         k          21
    
                   6        84       6(k+84)
    ----------------------------------------
           1       14      k+84     21+6(k+84)
    for (x-6) to be a factor, the remainder, 21 + 6(k+84), has to equal 0.
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