x³+8x²-2x-16

Factor x² out of the first two terms: x³+8x² becomes x²(x+8)

x²(x+8)-2x-16

Factor -2 out of the last two terms: -2x-16 becomes -2(x+8)

x²(x+8)-2(x+8)

Factor out (x+8) 

(x+8)(x²-2)

Edwin