Question

question 4 of 5

select the correct answer.

what is the completely factored form of this polynomial?

\\4x^4 + 12x^2 + 9\\

\\((2x^2 + 3)(2x^2 - 3)\\)

\\((3x^2 + 2)^2\\)

\\((3x^2 + 2)(3x^2 - 2)\\)

\\((2x^2 + 3)^2\\)

Explanation:

Identify the polynomial structure

$$ 4x^4 + 12x^2 + 9 = (2x^2)^2 + 2(2x^2)(3) + 3^2 $$

Apply the perfect square trinomial formula

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

$$ (2x^2 + 3)^2 $$

Answer:

• (A) \((2x^2 + 3)(2x^2 - 3)\)
• (B) \((3x^2 + 2)^2\)
• (C) \((3x^2 + 2)(3x^2 - 2)\)
• (D) \((2x^2 + 3)^2\) (Correct answer)