College Math Placement Practice Test 2025 – Comprehensive All-in-One Guide for Exam Success!

Question: 1 / 400

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

(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

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(x - 9)(x + 9)

(x - 9)(x + 1)

(x - 3)(x + 1)

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