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:

Step1: Recall Zero Product Property

The Zero Product Property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both). For the equation \(3(x - 4)(x + 5)=0\), we can apply this property. Since \(3\) is a non - zero constant (\(3
eq0\)), we focus on the factors \((x - 4)\) and \((x + 5)\).

Step2: Solve for \(x\) from each factor

• For the factor \((x - 4)\): Set \(x - 4=0\). By adding \(4\) to both sides of the equation, we get \(x=4\).
• For the factor \((x + 5)\): Set \(x + 5 = 0\). By subtracting \(5\) from both sides of the equation, we get \(x=-5\).

Answer:

\(x = 4\) or \(x=-5\) (corresponding to the option: \(x = 4\) or \(x=-5\))