Factor out the GCF. \( 3 x^{2}+9 x+24 \)

To factor out the **Greatest Common Factor (GCF)** from the expression \( 3x^{2} + 9x + 24 \), follow these steps: 1. **Identify the GCF of the coefficients:** - The coefficients are **3**, **9**, and **24**. - The GCF of **3**, **9**, and **24** is **3**. 2. **Factor out the GCF:** - Divide each term by **3**: \[ 3x^{2} \div 3 = x^{2}, \quad 9x \div 3 = 3x, \quad 24 \div 3 = 8 \] - Rewrite the expression with the GCF factored out: \[ 3x^{2} + 9x + 24 = 3(x^{2} + 3x + 8) \] 3. **Check if further factoring is possible:** - The quadratic inside the parentheses, \( x^{2} + 3x + 8 \), does not factor neatly over the real numbers because its discriminant is negative: \[ \Delta = 3^{2} - 4 \times 1 \times 8 = 9 - 32 = -23 \] - Since the discriminant is negative, the quadratic does not have real roots and cannot be factored further. **Final Factored Form:** \[ 3(x^{2} + 3x + 8) \]