Question

which binomial is a factor of $9x^2 - 64$?
○ $3x - 8$
○ $9x - 32$
○ $3x + 32$
○ $9x + 8$

Explanation:

Step1: Identify the formula

The expression \(9x^2 - 64\) is a difference of squares. The formula for factoring a difference of squares is \(a^2 - b^2=(a + b)(a - b)\).

Step2: Rewrite the expression

Rewrite \(9x^2\) as \((3x)^2\) and \(64\) as \(8^2\). So, \(9x^2 - 64=(3x)^2-8^2\).

Step3: Apply the formula

Using the difference of squares formula \(a^2 - b^2=(a + b)(a - b)\) with \(a = 3x\) and \(b = 8\), we get \((3x + 8)(3x - 8)\).

Answer:

A. \(3x - 8\)