To factor the expression [tex]\( x^3 - 1 \)[/tex], we can recognize that it is a difference of cubes. The standard formula for factoring a difference of cubes [tex]\( a^3 - b^3 \)[/tex] is given by:
[tex]\[ a^3 - b^3 = (a - b)(a^2 + ab + b^2) \][/tex]
In this specific problem, we can set [tex]\( a = x \)[/tex] and [tex]\( b = 1 \)[/tex]. Substituting these values into the formula, we have:
[tex]\[ x^3 - 1^3 = (x - 1)(x^2 + x \cdot 1 + 1^2) \][/tex]
[tex]\[ x^3 - 1 = (x - 1)(x^2 + x + 1) \][/tex]
Hence, the factored form of [tex]\( x^3 - 1 \)[/tex] is:
[tex]\[ (x - 1)(x^2 + x + 1) \][/tex]
So, the correct answer from the given options is:
[tex]\[ \boxed{(x - 1)(x^2 + x + 1)} \][/tex]
