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