To factor the expression x^3 + 8, recognize it as a sum of cubes, which can be expressed as (x + 2)(x^2 - 2x + 4). The formula used is a^3 + b^3 = (a + b)(a^2 - ab + b^2), with a = x and b = 2. To find factors, apply the Remainder and Factor Theorems by testing values like f(1), f(-1), and f(2) to identify roots. In this case, f(-2) = 0 indicates that x + 2 is a factor, and synthetic or long division can be used to determine the remaining factor.