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ParthKohli

  • 2 years ago

I don't understand this: is \(a + b\) a polynomial? They say that a polynomial is filled with constant coefficients and a single variable, that is, a polynomial is in the form \(f(x) = a + bx + cx^2 \cdots \)

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  1. ParthKohli
    • 2 years ago
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    On the other hand, it is a polynomial because it is filled with terms.

  2. amistre64
    • 2 years ago
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    a poly of one variable is expressed as your f(x) a poly of multiple variables is defined for: \[f(x_1,x_2,...,x_n)]\

  3. amistre64
    • 2 years ago
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    \[no latex?\]hmmm

  4. ParthKohli
    • 2 years ago
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    So this is a polynomial, right?

  5. ParthKohli
    • 2 years ago
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    I think you used ]\ instead of \] :-)

  6. amistre64
    • 2 years ago
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    lol, accursed typos!!

  7. amistre64
    • 2 years ago
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    yes, a+b is a polynomial of the form: \[f(a.b)=c_0a+c_1b+c_2a^2+c_3b^2+c_4a^2b+c_5ab^2+...\]

  8. ParthKohli
    • 2 years ago
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    Oh, I get where you are getting. The \(f(x)\) is just a specialized type of polynomial

  9. amistre64
    • 2 years ago
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    the variables are pretty much accounted for by adding up the appropriate:(a+b)^n parts, n=0,1,2,3,....

  10. amistre64
    • 2 years ago
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    yes

  11. ParthKohli
    • 2 years ago
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    But what are the polynomials in the form \(a + bx + cx^2 \cdots\) called?

  12. amistre64
    • 2 years ago
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    polynomials of a single variable is what id call them.

  13. ParthKohli
    • 2 years ago
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    OK - that clears it up. Thanks!

  14. amistre64
    • 2 years ago
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    http://www.wolframalpha.com/input/?i=polynomial a poly in one var ....

  15. amistre64
    • 2 years ago
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    think of a poly as a summation: \[f(x)=\sum_{n=0}^{N}(x)^n\] \[f(x,y)=\sum_{n=0}^{N}(x+y)^n\] \[f(x,y,z)=\sum_{n=0}^{N}(x+y+z)^n\] with something applied for constant coeefs

  16. ParthKohli
    • 2 years ago
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    That makes sense!

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