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12 February, 20:07

I don't understand the polynomials

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  1. 12 February, 22:29
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    Polynomial comes from poly - (meaning "many") and - nomial (in this case meaning "term") ... so it says "many terms"

    A polynomial can have:

    constants (like 3, - 20, or ½)

    variables (like x and y)

    exponents (like the 2 in y2), but only 0, 1, 2, 3, ... etc are allowed

    that can be combined using addition, subtraction, multiplication and division ...

    ... except ...

    ... not division by a variable (so something like 2/x is right out)

    So:

    A polynomial can have constants, variables and exponents,

    but never division by a variable.

    Also they can have one or more terms, but not an infinite number of terms.

    These are polynomials:

    3x

    x - 2

    -6y2 - (79) x

    3xyz + 3xy2z - 0.1xz - 200y + 0.5

    512v5 + 99w5

    5

    (Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!)

    These are not polynomials

    3xy-2 is not, because the exponent is "-2" (exponents can only be 0,1,2, ...)

    2 / (x+2) is not, because dividing by a variable is not allowed

    1/x is not either

    √x is not, because the exponent is "½" (see fractional exponents)

    But these are allowed:

    x/2 is allowed, because you can divide by a constant

    also 3x/8 for the same reason

    √2 is allowed, because it is a constant ( = 1.4142 ... etc)
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