Given that $f ( x )$ and $g ( x )$ and $h ( x )$ are linear polynomials and
$$f ( x ) \cdot g ( x ) \cdot h ( x ) = 0$$
prove that at least one of the following statements must be true;
(I) $f ( x ) \cdot g ( x ) = 0$,
(II) $g ( x ) \cdot h ( x ) = 0$,
(III) $f ( x ) \cdot h ( x ) = 0$.
For each of the three statements, give examples of polynomials for which that statement is true and the other two statements are false.