Question

what are the solutions to the equation \\(3(x - 4)(x + 5) = 0\\)?

\\(x = -4\\) or \\(x = 5\\)
\\(x = 3\\), \\(x = 4\\), or \\(x = -5\\)
\\(x = 3\\), \\(x = -4\\), or \\(x = 5\\)
\\(x = 4\\) or \\(x = -5\\)

Explanation:

Apply the zero product property

$$ 3(x - 4)(x + 5) = 0 \implies x - 4 = 0 \quad \text{or} \quad x + 5 = 0 $$

Solve each linear equation

$$
LATEXBLOCK0
$$

State the final solutions

$$ x = 4 \quad \text{or} \quad x = -5 $$

Answer:

• (A) \(x = -4\) or \(x = 5\)
• (B) \(x = 3\), \(x = 4\), or \(x = -5\)
• (C) \(x = 3\), \(x = -4\), or \(x = 5\)
• (D) \(x = 4\) or \(x = -5\) (Correct answer)