To factor the expression \( 4x^2 + 16x - 4 \) by taking out its greatest common factor (GCF), we first identify the GCF of all the terms in the expression.
The terms are \( 4x^2 \), \( 16x \), and \( -4 \).
The GCF of these coefficients (4, 16, and -4) is 4.
Now, we can factor out the GCF of 4 from each term:
\[ 4x^2 + 16x - 4 = 4(x^2 + 4x - 1) \]
So, the expression factored by taking out its greatest common factor is:
\[ 4(x^2 + 4x - 1) \]
If the choices given correspond to forms of the factored expression, please clarify those choices so that an appropriate answer can be selected.