Aultiply \( (x-4)(2 x+3) \) using the FOIL method. Select the answer choice howing the FOIL method products. B. \( (2 x+3)+(x-4)(2 x)+(2 x)(3) \) C. \( (x)(2 x)+3(x)+(-4)(2 x)+(-4)(3) \) D. \( (x-4)(2 x)+(x-4)(3) \)

To multiply \( (x - 4)(2x + 3) \) using the **FOIL** method, you apply the following steps: 1. **First**: Multiply the first terms in each binomial. 2. **Outer**: Multiply the outer terms. 3. **Inner**: Multiply the inner terms. 4. **Last**: Multiply the last terms in each binomial. Let's break it down: 1. **First**: \( x \cdot 2x = 2x^2 \) 2. **Outer**: \( x \cdot 3 = 3x \) 3. **Inner**: \( -4 \cdot 2x = -8x \) 4. **Last**: \( -4 \cdot 3 = -12 \) Combining these products, we get: \[ 2x^2 + 3x - 8x - 12 \] \[ = 2x^2 - 5x - 12 \] **Matching this process to the answer choices:** - **Option C** correctly represents the FOIL method by showing each of the four products: \[ (x)(2x) + 3(x) + (-4)(2x) + (-4)(3) \] **Therefore, the correct answer is Option C.** **Answer:** C. \( (x)(2 x)+3(x)+(-4)(2 x)+(-4)(3) \)