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Math Help - Differences

  1. #1
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    Differences

    I'm trying to find the fifth difference (f(x+1) - f(x)) of a regular polynomial f(x)=ax5+bx4+cx3+dx2+ex+f but I keep messing up, help please!
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Differences

    Try finding the first difference of a linear function, the second difference of a quadratic, the third difference of a cubic, and you should see a pattern emerge.
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  3. #3
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    Re: Differences

    I tried, but i keep messing up when I get the fifth difference. The equation Im trying to find wont correspond.
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Differences

    When I compute the differences I suggested above, the pattern that emerges suggest the nth difference of an n degree polynomial will be n!a_n. Proofs of this can be found online.
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