The polynomial x3 + 8 is equal to

(x + 2)(x2 – 2x + 4).
(x – 2)(x2 + 2x + 4).
(x + 2)(x2 – 2x + 8).
(x – 2)(x2 + 2x + 8)

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]".

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