Sure, let's factor the given polynomial step by step.
The polynomial we have is:
[tex]\[ 25x^2 - 144 \][/tex]
First, we recognize that this polynomial is a difference of squares. The difference of squares can be factored using the formula:
[tex]\[ a^2 - b^2 = (a + b)(a - b) \][/tex]
To apply this formula, we need to identify [tex]\( a \)[/tex] and [tex]\( b \)[/tex] such that:
[tex]\[ a^2 = 25x^2 \][/tex]
[tex]\[ b^2 = 144 \][/tex]
From [tex]\( a^2 = 25x^2 \)[/tex], we can see that:
[tex]\[ a = 5x \][/tex]
From [tex]\( b^2 = 144 \)[/tex], we can see that:
[tex]\[ b = 12 \][/tex]
Now substitute [tex]\( a = 5x \)[/tex] and [tex]\( b = 12 \)[/tex] back into the difference of squares formula:
[tex]\[ 25x^2 - 144 = (5x)^2 - (12)^2 = (5x + 12)(5x - 12) \][/tex]
Thus, the polynomial [tex]\( 25x^2 - 144 \)[/tex] factors into:
[tex]\[ (5x + 12)(5x - 12) \][/tex]
So, the correct answer is:
[tex]\[ \boxed{(5x + 12)(5x - 12)} \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{\text{B. } (5x+12)(5x-12)} \][/tex]
