Question

factor the following binomial completely.

(121x^2 - 1)

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

a. (121x^2 - 1 = \\) (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:

$$ 121x^2 - 1 $$

We can rewrite each term as a perfect square:

$$ 121x^2 = (11x)^2 $$

$$ 1 = (1)^2 $$

This fits the difference of squares formula:

$$ a^2 - b^2 = (a - b)(a + b) $$

where \( a = 11x \) and \( b = 1 \).

Step 2: Apply the formula

Substitute \( a = 11x \) and \( b = 1 \) into the formula:

$$ (11x - 1)(11x + 1) $$

Answer:

A. \( 121x^2 - 1 = (11x - 1)(11x + 1) \)