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.
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The Deep Dive
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. \( (x - 4)(x^2 + 1) \).
