(x^3 - 4x^2 - x) divided by (x - 4):
You would turn (x^3 - 4x^2 - x) into its factored form. We would take an x out of the whole rational equation ((x^3 - 4x^2 - x)) making the equation:
x(x^2 - 4x)
We would then factor the (x^2 - 4x) equation making it (x - 4)(x + 0). So the whole factored form of the equation, (x^3 - 4x^2 - x), is x((x - 4)(x + 0). So you would then divide the (x -4 ) from the new factored equation. Getting your answer, x(x + 0), which simplifies out to: x^2