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Math Help - Finding Unknown Coefficients of X (Another Problem)

  1. #1
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    Finding Unknown Coefficients of X (Another Problem)

    For all x, find the values of the constants a and b in:

    \displaystyle (x+a)(x^2+bx+2)=x^3+2x^2-5x-6

    Multiplied out i get:

    \displaystyle x^3+bx^2+2x+ax^2+abx+2a=x^3+2x^2-5x-6

    I then move the 2x over to the other side of the equation and cancel the cubed x's giving me:

    \displaystyle bx^2+ax^2+2a=-4x^2-x-6

    Then i'm stuck as i have two seperate variables attatched to a like power of x :?

    Any help would be great!
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  2. #2
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    Quote Originally Posted by BIOS View Post
    For all x, find the values of the constants a and b in:
    \displaystyle (x+a)(x^2+bx+2)=x^3+2x^2-5x-6
    Multiplied out i get:
    \displaystyle x^3+bx^2+2x+ax^2+abx+2a=x^3+2x^2-5x-6
    From that point you have:
    (a+b)x^2+(ab)x+2a=2x^2-7x-6

    But there must be something wrong with the question. It does not workout.
    Last edited by Plato; September 24th 2010 at 02:37 PM.
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  3. #3
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    Thanks for the reply.

    My Bad. Was doing the above while watching Dexter :P Okay so the format is still different from the problems i've done before. Does it matter what variable i equate in terms of order?

    Can i say:

    \displaystyle 2a=-6

    \displaystyle a=-3

    And then go from there? I tried but it doesn't work out :?

    Sorry that 5x in the original question should read x. Apologies.....
    Last edited by BIOS; September 24th 2010 at 02:43 PM. Reason: Mistake in Question
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  4. #4
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    With that correction then b=1.
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  5. #5
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    Okay that works fine with original question. Sorry for the typo thanks for the help! So basically you re-factor when you have an instance of more than one variable attached to a like power of x independently (to make it clearer) and it doesn't matter what order you equate i.e in the above i equated:

    \displaystyle 2a = -6

    \displaystyle a=-3

    Previously i could always equate the first term on either side of the equal sign whereas this time i obviously couldn't.
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