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Math Help - Factorising a polynomail over c

  1. #1
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    Factorising a polynomail over c

    How would one start this factorisation?

    P(z) = z^2 +(3 +2i)z +6i

    Would you just sub in values of z until you get P(z) to equal zero? Or is there a better way to approach this problem?

    I subbed in values til P(z) equals zero and I found -3 to be a root, but is there a more sophisticated way to solving this problem than just subbing in values until you get a zero?

    David.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    In general, if p(z)=az^2+bz+c\in\mathbb{C}[z]\quad (a\neq 0) then,

    p(z)=a(z-z_1)(z-z_2)

    where z_1,z_2 are the solutions of the quadratic equation az^2+bz+c=0 .
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  3. #3
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    Oh yeah so it's
    z^2 + 3z + 2zi + 6i
    z(z + 3) + 2i(z + 3)
    (z +2i)(z + 3)

    thanks
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