Question

find the complex zeros of the polynomial function. write f in factored form.

f(x)=x^3-10x^2+37x-52

Answer 1

first you need to graph on a graphing calculator to find a zero. once you do, you realize 4 is a zero so (x-4) is a solution. now you can either use long division or synthetic division. I chose synthetic.
4| 1 -10 37 -52
+4 -24 +52
= 1 -6 13 0
= x^2 -6x +13
then substitute that into the quadratic formula, find complex zeros
6 +/- the square root of -16 all over 2
simplifies to

3+4i or 3-4i

Answer 2

f in factored form is (x-4)(x-3-4i)(x-3+4i)