algebra
posted by sharday on .
Find the complex zeros of the polynomial function. Write f in factored form.
F(x)=x^38x^2+29x52
Use the complex zeros to write f in factored form
F(x)=____(reduce fractions and simplify roots)

testing for x = ±2, ± 4 and ±13, I found
f(4) = 0 , so x=4 is a zero, and x4 is a factor
x^38x^2+29x52 = (x4)(x^2  4x + 13) = 0
solving x^2  4x + 13 = 0 by completing the square (in this case faster than the formula)
x^2  4x + 4 = 13+4
(x2)^2 = 9
x2 = ± 3i
x = 2 ± 3i