Question

factor the following binomial completely.

(x^2 - 25)

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. (x^2 - 25 = \\) (factor completely.)
b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring special products

Step 1: Identify the pattern

The binomial is a difference of two perfect squares:

$$ x^2 - 25 = (x)^2 - (5)^2 $$

Step 2: Apply the difference of squares formula

Using the identity \( a^2 - b^2 = (a - b)(a + b) \):

$$ (x)^2 - (5)^2 = (x - 5)(x + 5) $$

Answer:

A. \( x^2 - 25 = (x - 5)(x + 5) \)