\[x^{2} - 10x - 24 =\]
\[= x^{2} - 10x + 25 - 49 =\]
\[= (x - 5)^{2} - 7^{2} =\]
\[= (x - 5 - 7)(x - 5 + 7) =\]
\[= (x - 12)(x + 2).\]