Question

Find the complex zeros of the polynomial function. Write f in factored form.
F(x)=x^3-8x^2+29x-52
Use the complex zeros to write f in factored form
F(x)=____(reduce fractions and simplify roots)

Answer 1

testing for x = ±2, ± 4 and ±13, I found
f(4) = 0 , so x=4 is a zero, and x-4 is a factor

x^3-8x^2+29x-52 = (x-4)(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
(x-2)^2 = -9
x-2 = ± 3i

x = 2 ± 3i