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Math Help - Factoring Polynomial w/ Prime Coefficient

  1. #1
    Junior Member ReneG's Avatar
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    Factoring Polynomial w/ Prime Coefficient

    I am trying to factor 3x^4 + 4x^3 -19x^2 -8x +12 into 4 factors to continue solving. I tried by grouping, but it didn't get me anywhere since 19 is prime (all zeros are rational). I also tried factoring out GCFs (x2 and x), but to no avail.
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  2. #2
    MHF Contributor
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    Re: Factoring Polynomial w/ Prime Coefficient

    Hey ReneG.

    Hint: There is a way to factor a quartic exactly using a formula figured out a while ago.

    https://en.wikipedia.org/wiki/Quarti...mula_for_roots
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  3. #3
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    Re: Factoring Polynomial w/ Prime Coefficient

    Try substituting various values of x, looking for a value that makes the polynomial zero.
    If x=a (say) makes the polynomial zero then (x-a) will be a factor.
    Factor this out and repeat the process on the lower degree polynomial.
    Start with x=1,2,-1,-2,... .
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  4. #4
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    Re: Factoring Polynomial w/ Prime Coefficient

    Quote Originally Posted by ReneG View Post
    I am trying to factor 3x^4 + 4x^3 -19x^2 -8x +12 into 4 factors to continue solving. I tried by grouping, but it didn't get me anywhere since 19 is prime (all zeros are rational). I also tried factoring out GCFs (x2 and x), but to no avail.
    Have a look at this.
    Thanks from ReneG
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