question 2 of 5

select all the correct answers.

which expressions are prime polynomials?

$x^2 - 3x - 10$

$x^3 - 512y^3$

$9y - 4y^2 + 12y^3$

$x^4 + 3y^2x - 1$

$x^2 - 9x + 3$

Question

question 2 of 5

select all the correct answers.

which expressions are prime polynomials?

$x^2 - 3x - 10$

$x^3 - 512y^3$

$9y - 4y^2 + 12y^3$

$x^4 + 3y^2x - 1$

$x^2 - 9x + 3$

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", "Factoring Trinomials", "Difference of Cubes" ] } ## Analyze factorability of each polynomial $$ \begin{aligned} &1.\quad x^2 - 3x - 10 = (x - 5)(x + 2) \quad \text{(Factorable)} \ &2.\quad x^3 - 512y^3 = x^3 - (8y)^3 = (x - 8y)(x^2 + 8xy + 64y^2) \quad \text{(Factorable)} \ &3.\quad 9y - 4y^2 + 12y^3 = y(12y^2 - 4y + 9) \quad \text{(Factorable)} \ &4.\quad x^4 + 3y^2x - 1 \quad \text{(No common factors, cannot be factored over the integers)} \ &5.\quad x^2 - 9x + 3 \quad \text{(No integers multiply to } 3 \text{ and add to } -9\text{, cannot be factored over the integers)} \end{aligned} $$

$\square\quad x^2 - 3x - 10$

$\square\quad x^3 - 512y^3$

$\square\quad 9y - 4y^2 + 12y^3$

$\square\quad x^4 + 3y^2x - 1$

$\square\quad x^2 - 9x + 3$

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

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Question

Explanation:

Analyze factorability of each polynomial

Answer: