Factor completely using the formula for sum \( x^{3}+1= \) Question Help: D Video

To factor \( x^{3} + 1 \), we can utilize the sum of cubes formula, which states that \( a^3 + b^3 = (a + b)(a^2 - ab + b^2) \). Here, \( a = x \) and \( b = 1 \). Applying the formula, we get: \[ x^{3} + 1 = (x + 1)(x^{2} - x \cdot 1 + 1^{2}) = (x + 1)(x^{2} - x + 1). \] So, the complete factorization of \( x^{3} + 1 \) is \( (x + 1)(x^{2} - x + 1) \). To ensure you've factored it correctly, it’s good to substitute \( x = -1 \) back into your factors and check if the original equation holds true. If \( (x+1) \) is a factor, substituting \( x = -1 \) should yield zero. It’s also a great practice to expand your factors back to see if they return to the original expression. Happy factoring!