Let's solve the given problem step-by-step.
We are given the expression [tex]\( 144 - 49x^2 \)[/tex].
We want to factorize this expression. Notice that it can be recognized as a difference of squares. The difference of squares formula states:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
Here:
[tex]\[ 144 \) is a perfect square, as \( 144 = 12^2 \)
\[ 49x^2 \) is also a perfect square, as \( 49x^2 = (7x)^2 \)
Using the difference of squares formula \( a^2 - b^2 = (a - b)(a + b) \), we can set \( a = 12 \) and \( b = 7x \). Thus,
\[ 144 - 49x^2 = 12^2 - (7x)^2 = (12 - 7x)(12 + 7x) \][/tex]
This means the factored form of [tex]\( 144 - 49x^2 \)[/tex] is:
[tex]\[ (12 - 7x)(12 + 7x) \)
Now, let's compare this to the given options to see which one matches. The options are:
1. \( 12 - 7x^2 \)
2. \( 72 - 7x^2 \)
3. \( 12 - 7x \)
4. \( 72 + 7x \)
Clearly, the factors we found are \( 12 - 7x \) and \( 12 + 7x \).
So, the factor that matches one of our derived factors is:
\[ \boxed{12 - 7x} \][/tex]
Thus, the correct factor of [tex]\( 144 - 49x^2 \)[/tex] from the given options is [tex]\( 12 - 7x \)[/tex].
