select the correct answer.

what is the factored form of $24y^5 + 3y^2$?

$3y^2(2y - 1)(4y^2 + 2y + 1)$

$3y^2(2y + 1)(4y^2 - 2y + 1)$

$(2y + 1)^2(4y^2 - 2y + 1)$

$(2y - 1)^2(4y^2 + 2y + 1)$

Question

select the correct answer.

what is the factored form of $24y^5 + 3y^2$?

$3y^2(2y - 1)(4y^2 + 2y + 1)$

$3y^2(2y + 1)(4y^2 - 2y + 1)$

$(2y + 1)^2(4y^2 - 2y + 1)$

$(2y - 1)^2(4y^2 + 2y + 1)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring Polynomials", "Sum of Cubes" ], "new_concepts": [], "current_concepts": [ "Factoring Polynomials", "Sum of Cubes" ] } ## Factor out the greatest common factor (GCF) $$ 24y^5 + 3y^2 = 3y^2(8y^3 + 1) $$ ## Apply the sum of cubes formula $$ \begin{aligned} 8y^3 + 1 &= (2y)^3 + 1^3\ &= (2y + 1)((2y)^2 - (2y)(1) + 1^2)\ &= (2y + 1)(4y^2 - 2y + 1) \end{aligned} $$ ## Combine the factors $$ 24y^5 + 3y^2 = 3y^2(2y + 1)(4y^2 - 2y + 1) $$

(A) $3y^2(2y - 1)(4y^2 + 2y + 1)$

(B) $3y^2(2y + 1)(4y^2 - 2y + 1)$

(C) $(2y + 1)^2(4y^2 - 2y + 1)$

(D) $(2y - 1)^2(4y^2 + 2y + 1)$

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

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QUESTION IMAGE

Question

Explanation:

Factor out the greatest common factor (GCF)

Apply the sum of cubes formula

Combine the factors

Answer: