Question

question 1 of 5

select the correct answer.

what is the factored form of this expression?

(x^3 + 27)

((x - 3)(x^2 + 3x + 9))

((x^2 + 3)(x - 3x + 9))

((x + 3)(x^2 - 3x + 9))

((x^2 - 3)(x + 3x + 9))

Explanation:

Identify the sum of cubes structure

$$ a^3 + b^3 = (a + b)(a^2 - ab + b^2) $$

Rewrite the given expression

$$ x^3 + 27 = x^3 + 3^3 $$

Apply the factoring formula

$$ x^3 + 3^3 = (x + 3)(x^2 - 3x + 3^2) = (x + 3)(x^2 - 3x + 9) $$

Answer:

• (A) \((x - 3)(x^2 + 3x + 9)\)
• (B) \((x^2 + 3)(x - 3x + 9)\)
• (C) \((x + 3)(x^2 - 3x + 9)\) (Correct answer)
• (D) \((x^2 - 3)(x + 3x + 9)\)