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Math Help - Is it a polynomial function?

  1. #1
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    Smile Is it a polynomial function?

    How do I know if this is a polynomial function?
    m(x)=(x^2-3x-4)/(x^2+1)

    Also...

    How would I find the zeros?
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  2. #2
    Senior Member mollymcf2009's Avatar
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    Polynomials functions are made of terms that have variables which are raised to whole-number exponents (or else the terms are just plain numbers); there are no square roots of variables, no fractional powers, and no variables in the denominator of any fractions.

    These are all polynomials: 6x (one term polynomial), 10x + 7 (bi-nomial, degree 1 polynomial), 7x^2 + 2x -6 (tri-nomial, degree 2 polynomial)

    The function you are asking about CAN be a polynomial, but in its present form it is NOT. It is currently a rational function (ratio/fraction) See if you can turn it into a polynomial. HINT: can you cancel anything?

    To find the zeroes, see if you can draw a graph of the function after you turn it into a polynomial
    Good luck!

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  3. #3
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    Quote Originally Posted by mollymcf2009 View Post
    [snip]The function you are asking about CAN be a polynomial, but in its present form it is NOT. It is currently a rational function (ratio/fraction) See if you can turn it into a polynomial. HINT: can you cancel anything?

    To find the zeroes, see if you can draw a graph of the function after you turn it into a polynomial
    Good luck!
    The function \frac{x^2 - 3x - 4}{x^2 + 1} is NOT a polynomial function.

    It CANNOT be 'turned into' a polynomial function by cancelling anything.

    The zeroes of \frac{x^2 - 3x - 4}{x^2 + 1} are found by solving x^2 - 3x - 4 = 0.

    Finding the zeroes of a function is usually required in order to actually sketch the graph of a function in the first place.
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