Question

solve $x^2 - 9 = 0$ by factoring. options: $x = 3, -3$; $x = 0, -9$; $x = 0, 9$; $x = 9$

Explanation:

Step1: Factor the equation

The equation \(x^2 - 9 = 0\) is a difference of squares, which factors as \((x - 3)(x + 3)=0\) (since \(a^2 - b^2=(a - b)(a + b)\) and here \(a = x\), \(b = 3\) as \(9 = 3^2\)).

Step2: Solve for \(x\)

Set each factor equal to zero:

• For \(x - 3 = 0\), we get \(x = 3\).
• For \(x + 3 = 0\), we get \(x=-3\).

Answer:

A. \(x = 3, -3\)