Factor the following high-degree polynomial completely.

To factor the polynomial \( 48x^6 - 3x^2 \) completely, first we can factor out the greatest common factor (GCF), which is \( 3x^2 \):

\[
48x^6 - 3x^2 = 3x^2(16x^4 - 1)
\]

Next, we notice that \( 16x^4 - 1 \) is a difference of squares:

\[
16x^4 - 1 = (4x^2)^2 - (1)^2 = (4x^2 - 1)(4x^2 + 1)
\]

Now we can further factor \( 4x^2 - 1 \) since it is also a difference of squares:

\[
4x^2 - 1 = (2x)^2 - (1)^2 = (2x - 1)(2x + 1)
\]

Putting it all together, we have:

\[
3x^2(16x^4 - 1) = 3x^2(4x^2 - 1)(4x^2 + 1) = 3x^2(2x - 1)(2x + 1)(4x^2 + 1)
\]

Thus, the complete factorization of \( 48x^6 - 3x^2 \) is:

\[
3x^2(2x - 1)(2x + 1)(4x^2 + 1)
\]

Among the provided response options, the correct answer is:

\[
3x^2(4x^2 + 1)(2x + 1)(2x - 1)
\]