Question 840292
We know that if -5i is a zero of the polynomial, then 5i must also be a zero.  If we rewrite these two zeros in factor form, we would have


(x + 5i)(x - 5i)


Now, let's expand that, by using the FOIL method.  This will give us:


{{{x^2 + 25}}}


Now, we have a factor of our original polynomial without the i's.  Now, we can use polynomial long division to divide our original function by {{{x^2 + 25}}}.  Doing this will give us:


{{{3x^2+7x-6}}}


Now, we can factor this polynomial.  This will give us, in factored form:


(3x - 2)(x + 3)


Setting each of these factors equal to zero, will give us our our other two zeroes:


3x - 2 = 0 -------> 3x = 2 -----> x = 2/3


and


x + 3 = 0 -----> x = -3


Since the highest degree of our original polynomial function is 4, and we now have found 4 zeroes, we are done.


Zereos:  -5i, 5i, 2/3, -3