How do you go about factoring $x^3-2x-4$? How do you factor $x^3-2x-4$?

To me, this polynomial seems unfactorable. 

But I check my textbook answer key, and the answer is $(x-2)(x^2+2x+2)$.

So I got to solve backward:

$$x(x^2-2)-4$$
And add some terms and subtract them later,
$$x(x^2+2x+2-2x-4)-4=0$$
$$x(x^2+2x+2)-4-2x^2-4x=0$$
$$x(x^2+2x+2)-2(x^2+2x+2)=0$$

But I would have thought of this way to factor if I didn't look at the answer key.
Rational root theorem  might be helpful, try to check whether factors of $-4$ satisfy the equation. 

By doing so, you would have encountered that $2$ is a root of the polynomial.
hint: $x-2$ is a factor. Can you finish it? (didn't look at your post)