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Math Help - Find all the zeros of this function

  1. #1
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    Find all the zeros of this function

    I am a little confused with this question
    Find all the zeros of the function and write the polynomial as a product of linear factors.
    g(x) = x^5 - 8x^4 + 28x^3 - 56x^2 + 64x - 32

    So I believe that I have to use synthetic division with a root of 2?

    1, -8, 28, -56, 64, -32
    _2_l____2,_-12,_32,_-48,__32__________
    1, -6, 16, -24, 16
    I hope you can understand that.

    Now I am confused with the next step. Do I use syntheic division again?

    Thanks for any help
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  2. #2
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    Quote Originally Posted by tsmith View Post
    I am a little confused with this question
    Find all the zeros of the function and write the polynomial as a product of linear factors.
    g(x) = x^5 - 8x^4 + 28x^3 - 56x^2 + 64x - 32

    So I believe that I have to use synthetic division with a root of 2?

    1, -8, 28, -56, 64, -32
    _2_l____2,_-12,_32,_-48,__32__________
    1, -6, 16, -24, 16
    I hope you can understand that.

    Now I am confused with the next step. Do I use syntheic division again?

    Thanks for any help
    x = 2 is a root. So express the quintic in the form (x - 2)(Quartic).

    x = 2 is a root of the quartic. So express the quartic in the form (x - 2)(Cubic).

    x = 2 is a root of the cubic. So express the cubic in the form (x - 2)(Quadratic).

    The quadratic is irreducible so the answer is (x - 2)^3 (Quadratic).
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