Write in factored form by factoring out the greatest common factor (or a negative common factor
\[
2 x^{7}-4 x^{6}+8 x^{5}
\]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $2 x^{7}-4 x^{6}+8 x^{5}=\square$
B. There is no common factor except 1.

Step 1 ：Given the expression \(2 x^{7}-4 x^{6}+8 x^{5}\).

Step 2 ：We need to factor out the greatest common factor from the expression.

Step 3 ：First, we identify the coefficients and powers of x in the terms of the expression. The coefficients are [2, -4, 8] and the powers are [7, 6, 5].

Step 4 ：Next, we find the greatest common factor (GCF) of the coefficients and the powers. The GCF of the coefficients is 2 and the GCF of the powers is 5.

Step 5 ：Then, we divide each coefficient by the GCF of the coefficients and subtract the GCF of the powers from each power. The factored terms are \(x^2\), \(-2x\), and 4.

Step 6 ：Finally, we write the expression in factored form by multiplying the GCF by the factored terms. The factored form of the expression is \(2x^5(x^2 - 2x + 4)\).

Step 7 ：\(\boxed{2 x^{7}-4 x^{6}+8 x^{5}=2x^5(x^2 - 2x + 4)}\)