College Math Placement Practice Test

What is the factored form of the expression x^2 - 9?

1. (x - 3)(x + 3)

2. (x - 9)(x + 9)

3. (x - 9)(x + 1)

4. (x - 3)(x + 1)

The correct answer is: (x - 3)(x + 3)

The expression \( x^2 - 9 \) is a classic example of a difference of squares, which can be expressed in factored form. The general formula for factoring a difference of squares is given by \( a^2 - b^2 = (a - b)(a + b) \). In this instance, \( x^2 \) serves as \( a^2 \) and \( 9 \) can be rewritten as \( 3^2 \). Thus, we can identify \( a \) as \( x \) and \( b \) as \( 3 \). Applying the difference of squares formula, we have: \[ x^2 - 9 = x^2 - 3^2 = (x - 3)(x + 3) \] By following this method, we arrive at the factored form \( (x - 3)(x + 3) \). This choice is valid because multiplying it out gives back the original expression: \[ (x - 3)(x + 3) = x^2 + 3x - 3x - 9 = x^2 - 9 \] This confirms that the factoring was performed correctly. The