Question 1-3 Alg 2 Midte Which points represent the zeros of the function \( f(x)=\left(x^{2}+2 x-8\right)(x-6) \) ? Select all that apply. \( (2,0) \) \( (6,0) \) \( (0,-8) \) \( (-4,0) \) \( (-6,0) \) \( (0,2) \) \( (0,8) \) \( \square \)

To determine the zeros of the function \( f(x) = (x^{2} + 2x - 8)(x - 6) \), we need to find the values of \( x \) that make \( f(x) = 0 \). ### Step 1: Set Each Factor to Zero 1. **First Factor:** \[ x^{2} + 2x - 8 = 0 \] Solve using the quadratic formula: \[ x = \frac{-2 \pm \sqrt{(2)^2 - 4(1)(-8)}}{2(1)} = \frac{-2 \pm \sqrt{4 + 32}}{2} = \frac{-2 \pm \sqrt{36}}{2} = \frac{-2 \pm 6}{2} \] So, the solutions are: \[ x = \frac{4}{2} = 2 \quad \text{and} \quad x = \frac{-8}{2} = -4 \] 2. **Second Factor:** \[ x - 6 = 0 \implies x = 6 \] ### Step 2: Identify the Zeros The zeros of the function \( f(x) \) are the points where \( f(x) = 0 \), which occur at: - \( x = 2 \) → Point: \( (2, 0) \) - \( x = -4 \) → Point: \( (-4, 0) \) - \( x = 6 \) → Point: \( (6, 0) \) ### Step 3: Compare with the Given Options From the list provided: - \( (2, 0) \) **✓** (Zero) - \( (6, 0) \) **✓** (Zero) - \( (-4, 0) \) **✓** (Zero) - \( (0, -8) \) ✗ (Not a zero) - \( (-6, 0) \) ✗ (Not a zero) - \( (0, 2) \) ✗ (Not a zero) - \( (0, 8) \) ✗ (Not a zero) ### **Conclusion** The points that represent the zeros of the function \( f(x) \) are: - \( (2, 0) \) - \( (6, 0) \) - \( (-4, 0) \) **Selected Points:** - \( \boxed{(2,\,0)} \) - \( \boxed{(6,\,0)} \) - \( \boxed{(-4,\,0)} \)