what is the factored form of $x^3 + 125$?

$(x^3 + 5)(x^6 - 5x^3 + 25)$
$(x^3 - 5)(x^6 + 5x^3 + 25)$
$(x + 5)(x^2 - 5x + 25)$
$(x - 5)(x^2 + 5x + 25)$

Question

what is the factored form of $x^3 + 125$?

$(x^3 + 5)(x^6 - 5x^3 + 25)$
$(x^3 - 5)(x^6 + 5x^3 + 25)$
$(x + 5)(x^2 - 5x + 25)$
$(x - 5)(x^2 + 5x + 25)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Sum of Cubes" ], "new_concepts": [], "current_concepts": [ "Sum of Cubes", "Factoring Polynomials" ] } ## Identify the terms as perfect cubes Using the *Sum of Cubes* knowledge point $$ \begin{aligned} x^3 &= (x)^3 \ 125 &= 5^3 \end{aligned} $$ ## Apply the sum of cubes formula Using the *Sum of Cubes* knowledge point $$ \begin{aligned} a^3 + b^3 &= (a + b)(a^2 - ab + b^2) \ x^3 + 5^3 &= (x + 5)(x^2 - 5x + 5^2) \ &= (x + 5)(x^2 - 5x + 25) \end{aligned} $$

(A) $(x^3 + 5)(x^6 - 5x^3 + 25)$

(B) $(x^3 - 5)(x^6 + 5x^3 + 25)$

(C) $(x + 5)(x^2 - 5x + 25)$

(D) $(x - 5)(x^2 + 5x + 25)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Sum of Cubes" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the terms as perfect cubes

Apply the sum of cubes formula

Answer: