college algebra
posted by ladybug .
find the complex zeros of the polynomial function. write f in factored form.
f(x)=x^310x^2+37x52

first you need to graph on a graphing calculator to find a zero. once you do, you realize 4 is a zero so (x4) 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 34i 
f in factored form is (x4)(x34i)(x3+4i)