select the correct answer.

what is the factored form of $x^9 + 27$?

$(x^3 - 3)(x^6 + 3x^3 + 9)$
$(x^3 + 3)(x^6 - 3x^3 + 9)$
$(x - 3)^3(x^6 + 3x^3 + 9)$
$(x + 3)^3(x^6 - 3x^3 + 9)$

Question

select the correct answer.

what is the factored form of $x^9 + 27$?

$(x^3 - 3)(x^6 + 3x^3 + 9)$
$(x^3 + 3)(x^6 - 3x^3 + 9)$
$(x - 3)^3(x^6 + 3x^3 + 9)$
$(x + 3)^3(x^6 - 3x^3 + 9)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Factoring" ], "new_concepts": [ "Sum of Cubes" ], "current_concepts": [ "Polynomial Factoring", "Sum of Cubes" ] } ## Rewrite the expression as a sum of cubes $$ x^9 + 27 = (x^3)^3 + 3^3 $$ ## Apply the sum of cubes factorization formula $$ a^3 + b^3 = (a + b)(a^2 - ab + b^2) $$ $$ \begin{aligned} (x^3)^3 + 3^3 &= (x^3 + 3)((x^3)^2 - (x^3)(3) + 3^2) \ &= (x^3 + 3)(x^6 - 3x^3 + 9) \end{aligned} $$

(A) $(x^3 - 3)(x^6 + 3x^3 + 9)$

(B) $(x^3 + 3)(x^6 - 3x^3 + 9)$

(C) $(x - 3)(x^6 + 3x^3 + 9)$

(D) $(x + 3)(x^6 - 3x^3 + 9)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Factoring" ] }

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QUESTION IMAGE

Question

Explanation:

Rewrite the expression as a sum of cubes

Apply the sum of cubes factorization formula

Answer: