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Math Help - dividing polynomial

  1. #1
    Newbie allywallyrus's Avatar
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    dividing a polynomial

    i'm not sure which forum this belongs in, but this seemed like the closest fit. the question is asking me to solve for x and i'm kinda stuck
    heres what i have:
    2x^3+6x^2-x=3
    so i brought the 3 over and found out -3 is a factor
    f(-3)=2(-3^3)+6(-3^2)-(-3)-3
    -54+54+3-3=0
    but then when i divide the initial equation by x+3 it end up with a zero and then i dont really know where to go from there
    ideas?
    Last edited by allywallyrus; March 16th 2009 at 01:03 PM. Reason: cleaned up formatting
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by allywallyrus View Post
    i'm not sure which forum this belongs in, but this seemed like the closest fit. the question is asking me to solve for x and i'm kinda stuck
    heres what i have:
    2x^3+6x^2-x=3
    so i brought the 3 over and found out -3 is a factor
    f(-3)=2(-3^3)+6(-3^2)-(-3)-3
    0=-54+54+3-3
    but then when i divide the initial equation by x+3 it end up with a zero and then i dont really know where to go from there
    ideas?
    Hi allywallyrus,

    First of all, -3 is not a factor. -3 is a zero (root) of f(x)=2x^3+6x^2-x-3

    x+3 is a factor.

    Using synthetic division, we can easily find the depressed polynomial in the 2nd degree.

    Code:
     
    -3 | 2  6  -1  -3
           -6   0   3
        -------------
         2  0  -1   0
    The depressed polynomial is 2x^2-1=0, which you can easily find the remaining 2 zeros.
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  3. #3
    Newbie allywallyrus's Avatar
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    oh, sorry about that
    thanks for the quick response, we never went over synthetic division so i've been doing it the long way.
    much appreciated!
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by allywallyrus View Post
    oh, sorry about that
    thanks for the quick response, we never went over synthetic division so i've been doing it the long way.
    much appreciated!
    You get the same quadratic polynomial if you use long division.
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