Usually, such a problem statement means we can group the first two terms and the last two terms

x^3 + 8x^2 - 2x - 16

= x^2(x+8) - 2(x+8)

= (x^2-2)(x+8)

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If the constant 2 in the first factor were a square, then it could be further factored.

x^3 + 8x^2 - 2x - 16

= x^2(x+8) - 2(x+8)

= (x^2-2)(x+8)

_____

If the constant 2 in the first factor were a square, then it could be further factored.