The answer is: [A]: (x + 2) (x² − 2x + 4).
Explanation:
Note the formula:
a³ + b³ = (a + b) (a² − ab + b²)
x³ + 8 can be written as x³ + 2³ ; since 2³ = 8
So, using the formula:
a³ + b³ = (a + b) (a² − ab + b²) ;
x³ + 8 ; or, x³ + 2³ ; can be factored; where a = x and b = 2.
→ Substitute these values for "a" and "b"; and rewrite:
→ x³ + 2³ = (x + 2) (x² - x*2 + 2²) ;
→ Simplify, and rewrite as:
→x³ + 8 = x³ + 2³ = (x + 2) (x² − 2x + 4) ;
→which is our first answer choice, "[A]".