Factor: \( 8+x^{3} \) A \( (2+x)\left(4-2 x+x^{2}\right) \) B \( (2+x)^{3} \) C \( (2-x)\left(4+2 x+x^{2}\right) \) D \( (2+x)\left(4+x^{2}\right) \)

To factor \( 8+x^{3} \), we can rewrite it as \( 8 + x^3 = 2^3 + x^3 \). This can be factored using the sum of cubes formula, which says that \( a^3 + b^3 = (a + b)(a^2 - ab + b^2) \). Here, \( a = 2 \) and \( b = x \). Applying the formula, we have: \[ (2 + x)(2^2 - 2 \cdot x + x^2) = (2 + x)(4 - 2x + x^2) \] Therefore, the answer is A: \( (2+x)(4-2 x+x^{2}) \). Now, talking a bit more about this concept, the sum of cubes is not just a trick; it's a foundational concept in algebra that helps us simplify polynomials efficiently. You can use it in various algebraic manipulations from homework problems to more complex equations. Additionally, keep in mind that common mistakes when factoring include overlooking the perfect cube structure or misapplying the sum or difference of cubes formulas. Always double-check the terms to ensure you've identified the correct factors! Happy factoring!