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Math Help - Representation of a given polynomial in factorial notation

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    Representation of a given polynomial in factorial notation

    Hi,
    Represent f(x)=$ 2x^4 -12x^3 +24x^2 - 30x +9 $ and its successive differences in factorial notation
    Solution:Let f(x) =$ 2x^4 - 12x^3 +24x^2 -30x +9 $
    =$2x^{(2)} +bx^{(3)} +cx^{(2)} +dx +9 $
    =2x(x-1)(x-2)(x-3) +bx(x-1)(x-2) +cx(x-1) +dx +9 where b,c and d are constants to be determined.
    Putting x=1, we get,
    -7=0+0+0+d+9
    $ \therefore $ d=-16
    Similarly, putting x=2 and x=3 in turn, we find c=2, b=0
    f(x)=$ 2x^{(4)}+2x^{(2)} - 16x^{(1)} + 9 $
    $ \Delta f(x)=8x^{(3)} + 4x -16 $
    $ \Delta^2 f(x)=24x^{(2)}+ 4 $
    $ \Delta^3 f(x)=48x $
    $\Delta^4 f(x)= 48 $

    Is this correct ?
    Reply is appreciated.
    Last edited by Vinod; March 17th 2014 at 08:06 AM.
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