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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.

  • Algebra -

    values I would try are
    ±1, ±3, ±1/2, and ±3/2

    on the second try
    f(-1) = -2-3+8-3 = 0
    so x+1 is a factor.
    by synthetic division I got
    2x^3 – 3x^2 – 8x – 3 = (x+1)(2x^2 - 5x -3)

    with a couple trial and error stabs, I factored the quadratic into (x-3)(2x+1)

    so the factors are

    of course I could have continued with the above values of a) and tried
    f(3), f(-3), f(1/2) etc
    and would have found
    f(3) and f(-1/2) also to result in zero.

  • Algebra -

    F(x) = (2x+1) (x+1) (x-3)

    F(x) =0
    F(x) = (2x+1) (x+1) (x-3)
    (2x+1) (x+1) (x-3) = 0

    Is this a good way to show the procedure?

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