If
\[ f(x) = x^3 - 3x^2 + 2x \qquad \qquad \qquad \ \]
When is f(x) = 0?
Factorise the right hand side
\[ \begin{align}
f(x) &= x(x^2 - 3x + 2) \\
\end{align}\ \]
x is a factor so x = 0 is a solution
\[ \begin{align}
f(0) &= (0)((0)^2 - 3(0) + 2) \\
&= 0
\end{align}\ \]
The solutions to the quadratic factor also make f(x) = 0
\[ \begin{align}
x^2 - 3x + 2 &= 0 \\
(x-2)(x-1) &= 0
\end{align}\ \]
so the zeroes of f(x) are x = 0, 1 and 2.