question 5 (multiple choice worth 2 points)
(02.03r mc)

which of the following is a factor of $x^3 - 1331$?

- $x - 11$
- $x^2 - 11x + 121$
- $x^2 + 22x + 121$
- none of the above

Question

question 5 (multiple choice worth 2 points)
(02.03r mc)

which of the following is a factor of $x^3 - 1331$?

- $x - 11$
- $x^2 - 11x + 121$
- $x^2 + 22x + 121$
- none of the above

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 and Difference of Cubes" ], "new_concepts": [], "current_concepts": [ "Sum and Difference of Cubes", "Factoring Polynomials Completely" ] } ## Identify the cube roots Using the *Sum and Difference of Cubes* knowledge point $$ \begin{aligned} &a^3 = x^3 \implies a = x\ &b^3 = 1331 \implies b = 11 \end{aligned} $$ ## Apply the difference of cubes formula Using the *Sum and Difference of Cubes* knowledge point $$ \begin{aligned} &a^3 - b^3 = (a - b)(a^2 + ab + b^2)\ &x^3 - 1331 = (x - 11)(x^2 + 11x + 121) \end{aligned} $$ ## Determine the correct factor Using the *Sum and Difference of Cubes* knowledge point $$ \text{Factors are } (x - 11) \text{ and } (x^2 + 11x + 121) $$

(A) $x - 11$

(B) $x^2 - 11x + 121$

(C) $x^2 + 22x + 121$

(D) None of the above

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

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QUESTION IMAGE

Question

Explanation:

Identify the cube roots

Apply the difference of cubes formula

Determine the correct factor

Answer: