\[x^{2} + 2x - 8 = x^{2} + 2x + 1 - 9 =\]
\[= (x + 1)^{2} - 9 =\]
\[= (x + 1 - 3)(x + 1 + 3) =\]
\[= (x - 2)(x + 4)\]