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Math Help - Algebra problems

  1. #1
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    Algebra problems

    I've got my head stuck around these 2 problems. I'm trying to factor these polynomials, but I just can seem to get them.

    The first one is f(x) = x^3 + x^2 - 8x - 6

    The 2nd one is f(x) = x^5 + 3x^4 - 4x^3 - 11x^2 - 3x + 2

    I'd appreciate any tips, thanks!
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  2. #2
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    For the second one, try dividing by a possible root. Try x-2 and/or x+1

    If it reduces down, then that's a root and you're on your way.

    \frac{x^{5}+3x^{4}-4x^{3}-11x^{2}-3x+2}{x-2}=x^{4}+5x^{3}+6x^{2}+x-1

    See?. That reduced down to a quartic. Try dividing that by another factor or some other tactic and whittle away at it.
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  3. #3
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    Is that the only way to go about factoring these?
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  4. #4
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    For 1.

    f(-3) = -27 + 9 + 24 - 6 = 0

    So (x+3) is a factor of f(x).

    By using long division,

    f(x) = (x+3) (x^2 - 2x - 2)

    Then do factories.


    Same for 2.
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  5. #5
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    why exactly did you do f(-3) for the first one? where did the -3 come from exactly. Sorry I'm posting on this thread when its not mine but I'm just interested in this problem.
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  6. #6
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    Quote Originally Posted by OzzMan View Post
    why exactly did you do f(-3) for the first one? where did the -3 come from exactly. Sorry I'm posting on this thread when its not mine but I'm just interested in this problem.
    Feel free, this helps me too!
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  7. #7
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    Well, it is not exactly f(-3). You’ve to take some values of x, like +1, -1, +2, -2………. After doing some exercise you can easily realize that what is the factor of f(x), without doing any rough.
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