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Math Help - Solve using Synthetic Division and the Given Root

  1. #1
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    Solve using Synthetic Division and the Given Root

    Solve the following equation using synthetic division, given the indicated root.

    <br />
x^3-10x^2 + 28x-24=0,r=2<br />

    Synthetic Division using the given root:

    <br />
x^3-10x^2+28x-24=(x+2)(x^2-8x+12)<br />

     <br />
(x^2-8x+12)=(x-6)(x-2)<br />

    Solution:

     <br />
(x+2)(x-6)(x-2)<br />

    I know my solution is wrong because multiplying back in does not result in the original answer.

    What am I doing wrong?

    I think that I'm performing an error in the begining with the synthetic division but I can't tell what I'm doing wrong.
    Last edited by MauiCormac; July 12th 2010 at 04:06 AM.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    The root is 2 NOT -2...
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  3. #3
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    Quote Originally Posted by MauiCormac View Post
    Solve the following equation using synthetic division, given the indicated root.

    <br />
x^3-10x^2 + 28x-24=0,r=2<br />

    Synthetic Division using the given root:

    <br />
x^3-10x^2+28x-24=(x+2)(x^2-8x+12)<br />
    You are wrong here: if x= 2 is a root then x- 2 is a factor, not x+ 2.

     <br />
(x^2-8x+12)=(x-6)(x-2)<br />

    Solution:

     <br />
(x+2)(x-6)(x-2)<br />

    I know my solution is wrong because multiplying back in does not result in the original answer.

    What am I doing wrong?

    I think that I'm performing an error in the begining with the synthetic division but I can't tell what I'm doing wrong.
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  4. #4
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    I know.

    I got it. Somone just explained it to me. The root is 2 which is one answer, and then when I solve I get (x-6)(x-2) and I forgot to make that = to 0.
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