Question

the polynomial \\(x^3 + 8\\) is equal to

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

Explanation:

Identify the sum of cubes structure

$$ x^3 + 8 = x^3 + 2^3 $$

Apply the sum of cubes formula

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

Substitute values into the formula

$$ x^3 + 2^3 = (x + 2)(x^2 - 2x + 2^2) = (x + 2)(x^2 - 2x + 4) $$

Answer:

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