Factor the following by grouping. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( x^{3}-4 x^{2}+x-4 x^{2}+x-4=\square \) B. The polynomial is prime.

When you factor by grouping, you typically want to group terms that can be factored out together. In this case, combine the terms like this: \( x^3 - 4x^2 + x - 4 = (x^3 - 4x^2) + (x - 4). \) Now, factor out the common terms in each group: 1. From the first group \( x^3 - 4x^2 \), you can factor out \( x^2 \): \( x^2(x - 4) \). 2. From the second group \( x - 4 \), you can factor out \( 1 \): \( 1(x - 4) \). Now, you have: \( x^2(x - 4) + 1(x - 4) \). Notice that \( (x - 4) \) is a common factor. Thus, factor it out: \((x - 4)(x^2 + 1)\). So, the complete expression is: A. \( (x - 4)(x^2 + 1) \).