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Math Help - Rational Zeros Theorem

  1. #1
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    Rational Zeros Theorem

    I have been given the equation:

    f(x) = 81x^7 + 72x^6 - 389x^5 - 360x^4 - 80x^3

    and asked to find a) and b) using the Rational Zeros Theorem

    a) Factor f(x) into linear factors.

    b) List the zeros of f(x) and their multiplicities


    I understand that to use the rational zeroes theorem requires that there is a constant term so I factor out x^3, but at that point it seems there are no rational zeros. Any thoughts?
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Shonard View Post
    I have been given the equation:

    f(x) = 81x^7 + 72x^6 - 389x^5 - 360x^4 - 80x^3

    and asked to find a) and b) using the Rational Zeros Theorem

    a) Factor f(x) into linear factors.

    b) List the zeros of f(x) and their multiplicities


    I understand that to use the rational zeroes theorem requires that there is a constant term so I factor out x^3, but at that point it seems there are no rational zeros. Any thoughts?
    The possible zeros are of the form \frac{p}{q} where p represents all the numbers that divide -80, and q represents all the integers that divide 81.

    This particular expression is a nightmare. Try \frac{-4}{9}
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  3. #3
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    Awesome that worked.

    I now have:

    (x + 4/9)(81x^3 + 36x^2 - 405x - 180)

    unfortunately this sequence is about as easy to work with as the first, is there any way to narrow down the possibility's?
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