Question

select all the correct answers. consider this product \\(\frac{x^2 - 4x - 21}{3x^2 + 6x} \cdot \frac{x^2 + 8x}{x^2 + 11x + 24}\\) which values are excluded values for the product? \\(\square\\ 2\\) \\(\square\\ -8\\) \\(\square\\ 0\\) \\(\square\\ 7\\) \\(\square\\ -3\\)

Explanation:

Step1: Identify Denominators

The denominators are \(3x^2 + 6x\), \(x^2 + 11x + 24\). Excluded values make any denominator zero.

Step2: Solve \(3x^2 + 6x = 0\)

Factor: \(3x(x + 2) = 0\). Solutions: \(x = 0\) or \(x = -2\) (but -2 not an option here).

Step3: Solve \(x^2 + 11x + 24 = 0\)

Factor: \((x + 3)(x + 8) = 0\). Solutions: \(x = -3\) or \(x = -8\).

Step4: Check Numerators? No, denominators only. So check options: 0 (from first denominator), -8 (from second), -3 (from second). 2 and 7 don't make denominators zero.

Answer:

-8, 0, -3 (corresponding checkboxes: -8, 0, -3)