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Math Help - find linear factors of this quartic expression

  1. #1
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    find linear factors of this quartic expression

    f(x)=x^4-7x^3+9x^2+7x-10
    f(1)=1^4-7*1^3+9*1^2+7*1-10=0
    x-1 is a factor, using long devision I have;
    f(x)=x^4-7x^3+9x^2+7x-10=(x-1)(x^3-6x^2+3x+10)=(x-1)g(x)
    g(2)=2^3-^*2^2+3*2+10=0
    so x-2 is a factor, using long devision again I get;
    f(x)=x^4-7x^3+9x^2+7x-10=(x-1)(x-2)(x^2+4x+11+(32/x-2))
    and now I'm stuck, please help
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  2. #2
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    You have two of them correctly. Now, since two of them can be factored out, you have a quadratic remaining which should be easier.

    \frac{x^{4}-7x^{3}+9x^{2}+7x-10}{(x-2)(x-1)}=x^{2}-4x-5

    You can factor that I am sure.
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  3. #3
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    Thanks but I'm not sure how you have factored them out? Sorry
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  4. #4
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    No its ok, you just divide the quartic by x-2 then divide the result buy x-1 to get that quadratic. Dont really know why but that works.
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