select the correct answer.

which expression is a prime polynomial?

$8x^7 - 9x + 12x^2$

$x + 9y^2$

$x^9 - y^5$

$3m + 9n$

Question

select the correct answer.

which expression is a prime polynomial?

$8x^7 - 9x + 12x^2$

$x + 9y^2$

$x^9 - y^5$

$3m + 9n$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Prime Polynomial", "Polynomial Factoring", "Difference of Squares" ], "new_concepts": [], "current_concepts": [ "Prime Polynomial", "Polynomial Factoring", "Difference of Squares" ] } ## Analyze factorability of each option $$ \begin{aligned} &\text{Option 1: } 8x^7 - 9x + 12x^2 = x(8x^6 - 9 + 12x) \quad (\text{Factorable by GCF } x) \ &\text{Option 2: } x + 9y^2 \quad (\text{No common factors, cannot be factored over the integers}) \ &\text{Option 3: } x^9 - y^6 = (x^3)^3 - (y^2)^3 = (x^3 - y^2)(x^6 + x^3y^2 + y^4) \quad (\text{Factorable as difference of cubes}) \ &\text{Option 4: } 3m + 9n = 3(m + 3n) \quad (\text{Factorable by GCF } 3) \end{aligned} $$ ## Identify the prime polynomial $$ x + 9y^2 \text{ cannot be factored into polynomials of lower degree with integer coefficients.} $$

(A) $8x^7 - 9x + 12x^2$

(B) $x + 9y^2$

(C) $x^9 - y^6$

(D) $3m + 9n$

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

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QUESTION IMAGE

Question

Explanation:

Analyze factorability of each option

Identify the prime polynomial

Answer: