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precalculus

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I'm going to do this on my own, but I would like to check mine against yours - give me today to work on it and I will be able to compare. List all possible rational zeros for the polynomial find all real zeros and factor completely. show work

f(x)=3x^4-29x^3+89x^2-75x-36
thank you.

  • precalculus - ,

    good for you

    Tried x + ±1, ± 2, ±3
    found f(3) = 0
    so by synthetic division
    (x-3)(3x^3 - 20x^2 + 29x + 12)
    found x = 4 works in 2nd bracket, so x-4 is a factor
    another synthetic division .....

    so far
    (x-3)(x-4)(3x^2 - 8x - 3)
    and the quadratic factored again
    = (x-3)9x-4(x-3)(3x + 1)
    = (x-4)(3x+1)(x-3)^2 , double root at x=3

    so x = - 1/3, 3, 4

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