Solve by factoring, then perform synthetic division. $${x^4 - 3x^3 + 3x^2 - x = 0}$$
$${x(x^3 - 3x^2 + 3x - 1)}$$
Now, we have to perform synthetic division, if I'm correct we get the 1 to divide by from the X outside of the parentheses from the second equation, which is above this paragraph, and is also the factored form of the first equation.
$$\frac{x - 3 + 3 - 1}{1}$$
The answer is ${x = 0, 1}$. Does the 0 come from the remainder, and do the 1 come from the divisor?

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