Factor the GCF from the polynomial. \[ 18 x^{3} y^{2}-16 x^{3} y-10 x^{2} y \]

To factor out the **Greatest Common Factor (GCF)** from the polynomial \[ 18 x^{3} y^{2} - 16 x^{3} y - 10 x^{2} y, \] follow these steps: 1. **Identify the GCF of the coefficients:** - **Coefficients:** 18, -16, -10 - The GCF of 18, 16, and 10 is **2**. 2. **Identify the GCF of the variables:** - **For \( x \):** The exponents are 3, 3, and 2. The smallest exponent is **2**, so the GCF for \( x \) is \( x^2 \). - **For \( y \):** The exponents are 2, 1, and 1. The smallest exponent is **1**, so the GCF for \( y \) is \( y \). 3. **Combine the GCF of coefficients and variables:** - **Overall GCF:** \( 2x^2y \). 4. **Factor out the GCF from each term:** \[ \begin{align*} 18x^3y^2 &= 2x^2y \cdot 9xy, \\ -16x^3y &= 2x^2y \cdot (-8x), \\ -10x^2y &= 2x^2y \cdot (-5). \end{align*} \] 5. **Write the factored form:** \[ 2x^2y (9xy - 8x - 5). \] **Final Answer:** \[ 2x^{2} y \left(9 x y - 8 x - 5\right) \]