Simplify \( (2 x+3)(x-4) \) A. \( \quad 2 x^{2}-8 \) B. \( 2 x^{2}+7 x-12 \) C. \( 2 x^{2}-11 x-12 \) D. \( 2 x^{2}-5 x-12 \)

To simplify \( (2 x+3)(x-4) \), we can use the distributive property (or the FOIL method). 1. Multiply the first terms: \( 2x \cdot x = 2x^2 \). 2. Multiply the outer terms: \( 2x \cdot -4 = -8x \). 3. Multiply the inner terms: \( 3 \cdot x = 3x \). 4. Multiply the last terms: \( 3 \cdot -4 = -12 \). Now, combine the like terms: \[ 2x^2 - 8x + 3x - 12 = 2x^2 - 5x - 12 \] So, the simplified expression is \( 2x^2 - 5x - 12 \), which corresponds to option D. **Final Answer: D. \( 2 x^{2}-5 x-12 \)**