Question

find all the real and complex zeros of the polynomial P(x)=x^4 -2x^3 -2x^2-2x-3

Answer 1

you know that anything more complicated than a quadratic is tough, so look for low-hanging roots: ±1,±2,±3. A little synthetic division yields

P(x) = (x-3)(x+1)(x^2+1)

now it's easy.