Question

completely factor the given polynomial, if possible. if the polynomial cannot be factored, type
f\ in the answer box.

\\25x^2 - 9\\

Explanation:

Identify the polynomial structure

We are given the binomial expression:

$$ 25x^2 - 9 $$

We observe that both terms are perfect squares. This matches the algebraic form of a difference of two squares.

Apply the difference of squares formula

Using the Difference of Squares knowledge point:
The formula is:

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

We rewrite each term as a perfect square:

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

$$ 9 = 3^2 $$

Thus, we identify \(a = 5x\) and \(b = 3\).

Write the factored form

Using the Difference of Squares knowledge point:
Substituting \(a = 5x\) and \(b = 3\) into the formula:

$$ (5x)^2 - 3^2 = (5x - 3)(5x + 3) $$

This expression is completely factored.

Answer:

Completely factor the given polynomial, if possible. If the polynomial cannot be factored, type "NF" in the answer box.

\(25x^2 - 9 =\) <blank>\((5x - 3)(5x + 3)\)</blank>