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Math parts homework

  1. Jan 23, 2008 #1
    1. The problem statement, all variables and given/known data
    [tex]x^2+4x-2=A(x+2)(x-2)+Bx(x-2)+Cx(x+2)[/tex]
    How to find A, B and C?


    2. Relevant equations
    Answer is A=1/2, B=-3/4, C=5/4.


    3. The attempt at a solution
    A+B+C=1
    A(2-2)+B(0-2)+C(0+2)=4
    A*2*(-2)+B*0*(-2)+C*0*2=-2

    A+B+C=1
    0A-2B+2C=4
    -4A+0B+0C=-2

    C=2+B
    A=1/2
    1/2+B+2+B=1
    2B=-3/2
    B=-3/4
    C=2-3/4=5/4
     
    Last edited: Jan 23, 2008
  2. jcsd
  3. Jan 23, 2008 #2
    I would start by "simplifying" the R.H. side and then compare it to the L.H. side. Thus:

    [tex] A(x+2)(x-2)+Bx(x-2)+Cx(x+2) = Ax^2 -4A +Bx^2 - 2Bx +Cx^2+2Cx = \dots = x^2+4x-2[/tex]
     
  4. Jan 23, 2008 #3

    HallsofIvy

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    You don't tell how you arrived at those "relevant equations". J.D.'s suggestion, multiply out the right side will work, but this is easier:
    Since x= 0, -2, or 2 will make one of the factors on the right 0, let x be each of those in turn;
    If x= 0, -2= -4A
    If x= 2, 10= 8C
    If x= -2, -6= -8B
     
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