Factor out the greatest common factor in the expression. \( 5 x^{4}-15 x^{3}+25 x^{2} \) Select the correct choice below and fill in any answer boxes within your choice. A. \( 5 x^{4}-15 x^{3}+25 x^{2}=\square \) B. The polynomial is prime.

To factor out the greatest common factor (GCF) from the expression \( 5x^{4} - 15x^{3} + 25x^{2} \), follow these steps: 1. **Identify the GCF of the coefficients:** - The coefficients are 5, -15, and 25. - The GCF of 5, 15, and 25 is **5**. 2. **Identify the GCF of the variable parts:** - The variable parts are \( x^{4} \), \( x^{3} \), and \( x^{2} \). - The lowest exponent is \( x^{2} \). 3. **Combine the GCFs:** - The overall GCF is \( 5x^{2} \). 4. **Factor out the GCF:** \[ 5x^{4} - 15x^{3} + 25x^{2} = 5x^{2}(x^{2} - 3x + 5) \] So, the correct choice is: **A.** \[ 5x^{4} - 15x^{3} + 25x^{2} = 5x^{2}(x^{2} - 3x + 5) \]