Questions: Factor the four-term polynomial by grouping. x^3 + 8x^2 + 4x + 32 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x^3 + 8x^2 + 4x + 32 = B. The polynomial is not factorable by grouping.

Solution Steps

To factor the four-term polynomial by grouping, we can follow these steps:

1. Group the terms in pairs.
2. Factor out the greatest common factor (GCF) from each pair.
3. If a common binomial factor appears, factor it out.

Group the polynomial \(x^3 + 8x^2 + 4x + 32\) into two pairs: \[ (x^3 + 8x^2) + (4x + 32) \]

Factor out the GCF from each pair: \[ x^2(x + 8) + 4(x + 8) \]

Notice that \((x + 8)\) is a common factor: \[ (x + 8)(x^2 + 4) \]

Final Answer