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