(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The polynomial f(z) is defined by

f(z) = z^{5}- 6z^{4}+ 15z^{3}- 34z^{2}+ 36z - 48

Show that the equation f(z) = 0 has roots of the form z = ix where x is real, and hence factorize f(z)

3. The attempt at a solution

So I know that you begin by factoring out (z-ix) from the function, but I'm not quite sure how to work that out. I can only figure out how to get the first and last terms in the first step:

f(z) = (z-ix)(z^{4}+ ....... - 48i/x)

How would you go about finding everything in between those two terms?

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# Homework Help: Factoring Complex Functions

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