Factor by grouping. \[ \begin{array}{l}x^{3}-5 x^{2}+5 x-25 \\ \text { A. } x^{3}-5 x^{2}+5 x-25= \\ \text { B. The polynomial is prime. }\end{array} \]

**A.** To factor the polynomial \( x^{3} - 5x^{2} + 5x - 25 \) by grouping, follow these steps: 1. **Group the terms:** \[ (x^{3} - 5x^{2}) + (5x - 25) \] 2. **Factor out the common factors from each group:** \[ x^{2}(x - 5) + 5(x - 5) \] 3. **Factor out the common binomial factor \((x - 5)\):** \[ (x^{2} + 5)(x - 5) \] So, the factored form of the polynomial is: \[ x^{3} - 5x^{2} + 5x - 25 = (x^{2} + 5)(x - 5) \] **B.** Since the polynomial can be factored as shown above, it is **not** prime. Answer: Problem A Answer The factored form is (x² + 5) multiplied by (x – 5). Thus, x³ − 5x² + 5x − 25 = (x² + 5)(x − 5)