In which of the following ways can you express the polynomial \(4x^2 - 9\) as a product of its factors?

In which of the following ways can you express the polynomial \(4x^2 - 9\) as a product of its factors?

• A. (2x - 3)(2x + 3)
• B. (2x - 2)(2x + 2)
• C. (4x + 3)(x - 3)
• D. (2x - 4)(2x + 3)

Answer: (A)

To express the polynomial \(4x^2 - 9\) as a product of its factors, we can recognize that this expression is a difference of squares. The general formula for a difference of squares is \(a^2 - b^2 = (a - b)(a + b)\). In this case, we can rewrite \(4x^2 - 9\) as \((2x)^2 - 3^2\). Here, \(a = 2x\) and \(b = 3\). According to the difference of squares formula, we can factor it as: \[ (2x - 3)(2x + 3) \] This factorization corresponds to the correct answer, as it captures the essence of the original polynomial by breaking it down into two products that, when multiplied together, return to the original expression \(4x^2 - 9\). Verifying this, we can expand \((2x - 3)(2x + 3)\): \[ (2x - 3)(2x + 3) = 2x \cdot 2x + 2x \cdot 3 - 3 \cd

To express the polynomial (4x^2 - 9) as a product of its factors, we can recognize that this expression is a difference of squares. The general formula for a difference of squares is (a^2 - b^2 = (a - b)(a + b)).

In this case, we can rewrite (4x^2 - 9) as ((2x)^2 - 3^2). Here, (a = 2x) and (b = 3). According to the difference of squares formula, we can factor it as:

[

(2x - 3)(2x + 3)

]

This factorization corresponds to the correct answer, as it captures the essence of the original polynomial by breaking it down into two products that, when multiplied together, return to the original expression (4x^2 - 9).

Verifying this, we can expand ((2x - 3)(2x + 3)):

[

(2x - 3)(2x + 3) = 2x \cdot 2x + 2x \cdot 3 - 3 \cd