\[(x - 1) \cdot \ *\ = x^{2} - 4x + 3\]
\[x^{2} - 4x + 3 = x^{2} - x - 3x + 3 =\]
\[= x(x - 1) - 3 \cdot (x - 1) =\]
\[= (x - 1)(x - 3)\]
\[(x - 1) \cdot \ *\ = (x - 1)(x - 3)\]
\[\Longrightarrow \ *\ = (x - 3).\]