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Algebra 2

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Factor f(x)=x^4+x^3-8x^2+6x+36 completely

  • Algebra 2 - ,

    If there is a rational root, it would be +or- 1,2,3,4,6,8 or 12.
    x = -2 works, so x+2 is a factor.
    So, after one factoring step, and a bit of polynomial long division, you have
    (x+2)(x^3 -x^2 -6x +18) = 0

    Next, use the rational root theorm on the cubic factor. You will find that -3 is a root, making (x+3) a factor.

    So now you have
    x^4+x^3-8x^2+6x+36
    (x+2)(x+3)(x^2 -4x +6)

    The remaining two factors are complex conjugates.

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