Question

select the correct answer.

what is the completely factored form of this polynomial?
\\(x^4 + 12x^2 + 32\\)

\\((x^2 + 4)(x + 2)(x + 4)\\)
\\((x^2 + 4)(x^2 + 8)\\)
\\((x + 4)(x + 8)\\)
\\((x + 2)(x - 2)(x^2 + 8)\\)

Explanation:

Substitute to form a quadratic equation

$$ \text{Let } u = x^2 $$

$$ u^2 + 12u + 32 $$

Factor the quadratic expression

$$ (u + 4)(u + 8) $$

Substitute back the original variable

$$ (x^2 + 4)(x^2 + 8) $$

Answer:

• (A) \((x^2 + 4)(x + 2)(x + 4)\)
• (B) \((x^2 + 4)(x^2 + 8)\) (Correct answer)
• (C) \((x + 4)(x + 8)\)
• (D) \((x + 2)(x - 2)(x^2 + 8)\)