Factor by grouping. \[ 2 x^{3}-x^{2}-16 x+8 \]

Step 1 ：Factor the expression \(2 x^{3}-x^{2}-16 x+8\) by grouping.

Step 2 ：Group the terms as follows: \(2x^3 - x^2\) and \(-16x + 8\).

Step 3 ：Factor out the greatest common factor (GCF) from each group. The GCF of the first group is \(x^2\), and the GCF of the second group is 8.

Step 4 ：After factoring out the GCF, we should have two identical binomial factors. If we do, then we can factor by grouping. If not, then the expression cannot be factored by grouping.

Step 5 ：The factored form of the expression is \((2x - 1)(x^{2} - 8)\). This matches our expectation, as we factored out \(x^2\) from the first group and 8 from the second group, and the resulting binomial factors were the same.

Step 6 ：Final Answer: The factored form of the expression \(2 x^{3}-x^{2}-16 x+8\) by grouping is \(\boxed{(2x - 1)(x^{2} - 8)}\).