1)) Which polynomial has zeros at \( x=-4, x=-2, x=1 \), and \( x=3 \) ? \( (x+4)^{2}(x-1)^{3} \) \( (x-4)^{2}(x+1)^{3} \) \( (x-4)(x-2)(x+1)(x+3) \) \( (x+4)(x+2)(x-1)(x-3) \)

To determine which polynomial has zeros at \( x = -4, x = -2, x = 1 \), and \( x = 3 \), let's analyze each option: 1. **Option A:** \( (x + 4)^{2}(x - 1)^{3} \) - **Zeros:** - \( x = -4 \) (with multiplicity 2) - \( x = 1 \) (with multiplicity 3) - **Missing Zeros:** \( x = -2 \) and \( x = 3 \) 2. **Option B:** \( (x - 4)^{2}(x + 1)^{3} \) - **Zeros:** - \( x = 4 \) (with multiplicity 2) - \( x = -1 \) (with multiplicity 3) - **Missing Zeros:** \( x = -4, x = -2, x = 1, \) and \( x = 3 \) 3. **Option C:** \( (x - 4)(x - 2)(x + 1)(x + 3) \) - **Zeros:** - \( x = 4 \) - \( x = 2 \) - \( x = -1 \) - \( x = -3 \) - **Missing Zeros:** \( x = -4, x = -2, x = 1, \) and \( x = 3 \) 4. **Option D:** \( (x + 4)(x + 2)(x - 1)(x - 3) \) - **Zeros:** - \( x = -4 \) - \( x = -2 \) - \( x = 1 \) - \( x = 3 \) - **All Required Zeros Present** **Conclusion:** The correct polynomial that has zeros at \( x = -4, x = -2, x = 1 \), and \( x = 3 \) is: **\( (x + 4)(x + 2)(x - 1)(x - 3) \)** **Answer:** \( (x+4)(x+2)(x-1)(x-3) \)