find real and complex 0
posted by Armando .
Find the real and complex zeros of the following function. Please show all of your work.
f(x) = x^3 + 2x^2  6x + 8

f(±1) ≠ 0
f(±2) ≠ 0
but f(4) = 0
so x+4 is a factor
I then used synthetic division to get
(x+4)(x^2  2x + 2) = 0
the real root is x = 4
Use the quadratic formula to get the two complex roots of
1+i and 1i 
f(x)=x^3+4x^22x^28x+2x+8=(x^3+4x^2)
(2x^2+8x)+(2x+8)=x^2(x+4)2x(x+4)+2(x+4)=
(x+4)(x^22x+2)
x+4=0 => x=4
or
x^22x+2=0 => x=1+i or x=1i