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Math Help - Factoring a polynomial

  1. #1
    Junior Member ReneG's Avatar
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    Factoring a polynomial

    I need help factoring x^5+2x^3-x^2-2

    I tried it by grouping (x^5 - x^2) + (2x^3 -2)

    Then I got x^2(x^3 - 1) + 2(x^3 - 1)

    Thus my final answer was (x^3 - 1)(x^2+2)

    From there, I had no clue what to do. My text book says the correct answer is (x^2+2)(x-1)(x^2+x+1) but I just have no clue how they got there.

    Any help would be appreciated, thanks.
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  2. #2
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    Re: Factoring a polynomial

    Reneg

    continue the factorization process. and factorize the (x^3-1) it will give you (x-1)(x^2+x+1). therefore the polynomial after factorization becomes
    (x^2+2)(x-1)(x^2+x+1).
    now how to factorize the x^3-1 ..the (x-1) is a factor of the polynomial x^3 -1 therefore dividing by (x-1) or simply use Horner's method
    (Horner's method - Wikipedia, the free encyclopedia ) you will get the result .

    MINOAS
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  3. #3
    Junior Member ReneG's Avatar
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    Re: Factoring a polynomial

    I just don't see how you can factor out x - 1 from (x^3 - 1)(x^2 + 2) because there is no greatest common factor other than 1
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  4. #4
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    Re: Factoring a polynomial

    Quote Originally Posted by ReneG View Post
    I just don't see how you can factor out x - 1 from (x^3 - 1)(x^2 + 2) because there is no greatest common factor other than 1

    (x^3-1)=(x-1)(x^2+x+1) the difference of two cubes.
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  5. #5
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    Re: Factoring a polynomial

    Do you know how to multiply polynomials? What do you get when multiply (x- 1)(x^2+ x+ 1)?
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  6. #6
    Junior Member ReneG's Avatar
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    Re: Factoring a polynomial

    Oh wow, completely forgot about that rule. Seeing 1 as a cube root of 1 wasn't really intuitive for me at first, thanks!
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