Solve x³ - 8

Step-by-step solution

1. Recognise as difference of cubes: $x^3 - 8 = x^3 - 2^3$.

2. Apply the identity $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ with $a = x$, $b = 2$.

3. Result: $(x - 2)(x^2 + 2x + 4)$.

4. The trinomial factor $x^2 + 2x + 4$ has discriminant $4 - 16 = -12 < 0$, so it does not factor further over the reals.