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Math Help - factorosation of polynomials

  1. #1
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    factorosation of polynomials

    Hi the question says If z-3i is a factor of 2z^4-4z^3+21z^2-36z+27, find the remaining factors.

    I tried doing long division by dividing it by 2z+9 but i get a crazy fraction answer with a remainder which looked wrong, is their another way i can approach this.? and im working in the chapter factorasation of polynomials of C. someone suggested synthetic division but when i used that with 3i, i got zero as a answer

    The answer in the book is z+3i, z-1 (plus+, minus-) 1 (over) root2i

    Please can you guys try to answer this i spend like half a day trying to figure this out.

    thanks
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  2. #2
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    Why would you divide by \displaystyle 2z + 9? You're supposed to divide by \displaystyle z^2 + 9...

    You already asked this question and it was answered here... http://www.mathhelpforum.com/math-he...al-171814.html
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  3. #3
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    Quote Originally Posted by iFuuZe View Post
    Hi the question says If z-3i is a factor of 2z^4-4z^3+21z^2-36z+27, find the remaining factors.

    I tried doing long division by dividing it by 2z+9 but i get a crazy fraction answer with a remainder which looked wrong, is their another way i can approach this.? and im working in the chapter factorasation of polynomials of C. someone suggested synthetic division but when i used that with 3i, i got zero as a answer

    The answer in the book is z+3i, z-1 (plus+, minus-) 1 (over) root2i

    Please can you guys try to answer this i spend like half a day trying to figure this out.

    thanks
    All the coefficients are real and so the conjugate root theorem can be used. Therefore z + 3i is a factor. Therefore (z + 3i)(z - 3i) = z^2 + 9 is a factor. Divide z^2 + 9 into the polynomial to get the quadratic factor and then factorise it.
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