Question

which is a factor of $144 - 49x^2$?
$\bigcirc\\ 12 - 7x^2$
$\bigcirc\\ 72 - 7x^2$
$\bigcirc\\ 12 - 7x$
$\bigcirc\\ 72 + 7x$

Explanation:

Step1: Identify the formula

The expression \(144 - 49x^2\) 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 terms as squares

We can rewrite \(144\) as \(12^2\) and \(49x^2\) as \((7x)^2\). So, \(144 - 49x^2 = 12^2-(7x)^2\).

Step3: Apply the difference of squares formula

Using the formula \(a^2 - b^2=(a + b)(a - b)\) with \(a = 12\) and \(b = 7x\), we get:
\(12^2-(7x)^2=(12 + 7x)(12 - 7x)\)
So, one of the factors is \(12 - 7x\).

Answer:

12 - 7x (corresponding to the option "12 - 7x")