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dietrich_harmon

  • 3 years ago

Is the difference of two polynomials always a polynomial? Explain.

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  1. dietrich_harmon
    • 3 years ago
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    @Lilith

  2. Shadowys
    • 3 years ago
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    take this \(x^2 +x+2\) and \(x^2 +x+4\) are their difference a polynomial?

  3. dietrich_harmon
    • 3 years ago
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    ?

  4. Shadowys
    • 3 years ago
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    the two expressions are polynomials rite?

  5. dietrich_harmon
    • 3 years ago
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    yes

  6. Shadowys
    • 3 years ago
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    but subtracting the second from the first, gives us an integer, which is not a polynomial. This is a counter example

  7. dietrich_harmon
    • 3 years ago
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    so the answer is

  8. Shadowys
    • 3 years ago
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    It is shown that it's no.

  9. findme
    • 3 years ago
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    actually it is yes

  10. LogicalReason
    • 3 years ago
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    Hmm ... I believe that integers are polynomials. An integer is simply a polynomial of degree zero.

  11. Shadowys
    • 3 years ago
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    well, it seems so...though that would means any expression is a polynomial as long as the degree is a positive integer

  12. findme
    • 3 years ago
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    f(x)=0 f(x)=-3 are both polynomials to get the definition of polynomial: http://en.wikipedia.org/wiki/Polynomial

  13. findme
    • 3 years ago
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    degree is non-negative, so it can be 0 degree

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