Check each factorization to find the polynomial that does not have its GCF correctly factored out. Choose the correct answer below. A. \( 15 x^{2}+12 x+9=3\left(5 x^{2}+4 x+3\right) \) B. \( 12 x^{2}+8 x=4 x(3 x+2) \) C. \( 4 x^{4}+12 x^{3}+18 x^{2}=2 x^{2}\left(2 x^{2}+6 x+9\right) \) D. \( 16 x^{5}+24 x^{2}=4 x^{2}\left(4 x^{3}+6\right) \)

Let's evaluate each option to determine if the Greatest Common Factor (GCF) has been correctly factored out. **Option A:** \[ 15x^{2} + 12x + 9 = 3(5x^{2} + 4x + 3) \] - **GCF Calculation:** The GCF of \(15\), \(12\), and \(9\) is \(3\). - **Verification:** \(3(5x^{2} + 4x + 3) = 15x^{2} + 12x + 9\). **This is correct.** **Option B:** \[ 12x^{2} + 8x = 4x(3x + 2) \] - **GCF Calculation:** The GCF of \(12x^{2}\) and \(8x\) is \(4x\). - **Verification:** \(4x(3x + 2) = 12x^{2} + 8x\). **This is correct.** **Option C:** \[ 4x^{4} + 12x^{3} + 18x^{2} = 2x^{2}(2x^{2} + 6x + 9) \] - **GCF Calculation:** The GCF of \(4x^{4}\), \(12x^{3}\), and \(18x^{2}\) is \(2x^{2}\). - **Verification:** \(2x^{2}(2x^{2} + 6x + 9) = 4x^{4} + 12x^{3} + 18x^{2}\). **This is correct.** **Option D:** \[ 16x^{5} + 24x^{2} = 4x^{2}(4x^{3} + 6) \] - **GCF Calculation:** The GCF of \(16x^{5}\) and \(24x^{2}\) is \(8x^{2}\). - **Verification:** \(4x^{2}(4x^{3} + 6) = 16x^{5} + 24x^{2}\). **This is incorrect because the correct GCF should be \(8x^{2}\), not \(4x^{2}\).** **Conclusion:** Option **D** does not correctly factor out the GCF. **Answer:** D