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Consider the polynomial
f(x) = 2x^3 – 3x^2 – 8x – 3.

(a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial.


(b) Find all of the zeros of the given polynomial. Be sure to show work, explaining how you have found them.

  • Math -

    the rational zero theorem states that all rational zeroes of the given polynomial, the numerators have the form ±(factors of constant term) and the denominators have the form ±(factors of the coefficient of the highest term).
    See for example:
    http://mathworld.wolfram.com/RationalZeroTheorem.html
    In the given case,
    constant term = -3,
    coeff. of highest term = 2
    Possible rational zeroes are therefore:
    1, 3, 1/2, 3/2, -1, -3, -1/2, -3/2
    I will leave it to you to factorize the given polynomial to get the actual zeroes.
    You are welcome to post your answer for verification.

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