f(x) = x^4-x^3+0x^2-2x-4
Factoring, using synthetic division:
! 1 -1 0 -2 -4 Fourth degree
x+1→-1 ! -1 2 -2 4
---------------------------------
! 1 -2 2 -4 0 Third degree
x-2 → 2 ! 2 0 4
---------------------------------
1 0 2 0 Second degree
1x^2+0x+2 = x^2+2
f(x)=x^4-x^3-2x-4=(x+1)(x-2)(x^2+2)
x^2+2=0
Solving for x:
x^2+2-2=0-2
x^2=-2
sqrt(x^2)=+- sqrt(-2)
x=+- sqrt[(2)(-1)]
x=+- sqrt(2) sqrt(-1); sqrt(-1)=i
x=+- sqrt(2) i
f(x)=x^4-x^3-2x-4=(x+1) (x-2) [x-sqrt(2) i] [x+sqrt(2) i)]
