use the given zeros to find the remaining zeros of the function

Question

h(x)=x^4-9x^3+12x^2+138x-1360
zero:3-5i

enter the remaining zeros of f

please show work

Answer 1

(3 - 5i) and (3+5i)

therefore divide by product(x-3+5i) and (x-3-5i)
or
(x^2 - 6 x + 34)
so do long division

x^4-9x^3+12x^2+138x-1360
-------------------------
x^2 - 6 x + 34

which is (x^2-3x-40) whew, no remainder

find the two zeros of that

x = [ 3 +/- sqrt (9+160)]/2
= [3+/-13]/2
= -5 and 8

so in the end
-5
+8
-3-5i
-3+5i

Answer 2

That was fun :)

Answer 3

-5
+8
3-5i
3+5i