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Math Help - Factoring question

  1. #1
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    Factoring question

    Hi,

    What is the best method to go about factoring this x^6+6x^4+10x^2+8? Can this be done by grouping? I tried to do rational root tests but it appears as though it does not have any rational roots.

    Thanks for your help,
    James
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  2. #2
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    Quote Originally Posted by james121515 View Post
    Hi,

    What is the best method to go about factoring this x^6+6x^4+10x^2+8? Can this be done by grouping? I tried to do rational root tests but it appears as though it does not have any rational roots.

    Thanks for your help,
    James

    Might be helpful to say a = x^2 making the whole thing cubic instead.
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  3. #3
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    Quote Originally Posted by james121515 View Post
    Hi,

    What is the best method to go about factoring this x^6+6x^4+10x^2+8? Can this be done by grouping? I tried to do rational root tests but it appears as though it does not have any rational roots.

    Thanks for your help,
    James
    y = x^6+6x^4+10x^2+8 > 0 for all x ... no real roots.
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  4. #4
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    Well

    Thats an expression you have no = sign anywhere.
    Also it doesn´t have any x intercepts so it doesn´t factor.
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  5. #5
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    It factors to (x^2+2)^3. I'm curious as to what method you use to do it.
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  6. #6
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    Quote Originally Posted by james121515 View Post
    It factors to (x^2+2)^3. I'm curious as to what method you use to do it.
    x^6+6x^4+10x^2+8

    make a = x^2 now

    a^3+6a^2+10a+8

    Then employee the factor theorem checking positive and negative factors of 8.

    Spoiler:
    a = -2
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