\[x^{2} - 4x - 21 =\]
\[= x^{2} - 4x - 25 + 4 =\]
\[= (x - 2)^{2} - 25 =\]
\[= (x - 2 - 5)(x - 2 + 5) =\]
\[= (x - 7)(x + 3)\]