select the correct answer.

which expression is a prime polynomial?

$8x^7 - 9x + 12x^2$
$3m + 9n$
$x + 9y^2$
$x^9 - y^6$

Question

select the correct answer.

which expression is a prime polynomial?

$8x^7 - 9x + 12x^2$
$3m + 9n$
$x + 9y^2$
$x^9 - y^6$

Accepted Answer

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

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

(B) $3m + 9n$

(C) $x + 9y^2$

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

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

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QUESTION IMAGE

Question

Explanation:

Analyze the factorability of each option

Identify the prime polynomial

Answer: