which of the following are prime polynomials?

$5j + 15$

$7j + 28$

$-2$

$4j$

Question

which of the following are prime polynomials?

$5j + 15$

$7j + 28$

$-2$

$4j$

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": [ "Prime Polynomials", "Polynomial Factoring" ], "current_concepts": [ "Prime Polynomials", "Polynomial Factoring" ] } ## Analyze the definition of a prime polynomial A polynomial with integer coefficients is prime if it cannot be factored into a product of lower-degree polynomials with integer coefficients, and its terms share no common integer factors other than $\pm 1$. Monomials and constant polynomials are generally not classified as prime polynomials. ## Test each given option for factorability $$ \begin{aligned} &5j + 15 = 5(j + 3) \quad \text{(not prime, has common factor 5)} \ &7j + 28 = 7(j + 4) \quad \text{(not prime, has common factor 7)} \ &-2 \quad \text{(constant, not a prime polynomial)} \ &4j \quad \text{(monomial, not a prime polynomial)} \end{aligned} $$ ## Determine the correct selection None of the given options are prime polynomials.

(A) $5j + 15$

(B) $7j + 28$

(C) $-2$

(D) $4j$

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

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QUESTION IMAGE

Question

Explanation:

Analyze the definition of a prime polynomial

Test each given option for factorability

Determine the correct selection

Answer: