what is the factored form of $24x^6 + 3$?

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

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

$(6x^2 + 1)(4x^4 - 6x^2 + 1)$

$(6x^2 - 1)(4x^4 + 6x^2 + 1)$

Question

what is the factored form of $24x^6 + 3$?

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

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

$(6x^2 + 1)(4x^4 - 6x^2 + 1)$

$(6x^2 - 1)(4x^4 + 6x^2 + 1)$

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" ], "new_concepts": [ "Sum of Cubes" ], "current_concepts": [ "Factoring Polynomials", "Sum of Cubes" ] } ## Factor out the greatest common factor $$ 24x^6 + 3 = 3(8x^6 + 1) $$ ## Apply the sum of cubes formula $$ \begin{aligned} a^3 + b^3 &= (a + b)(a^2 - ab + b^2) \ 8x^6 + 1 &= (2x^2)^3 + 1^3 \ &= (2x^2 + 1)((2x^2)^2 - (2x^2)(1) + 1^2) \ &= (2x^2 + 1)(4x^4 - 2x^2 + 1) \end{aligned} $$ ## Combine the factored components $$ 24x^6 + 3 = 3(2x^2 + 1)(4x^4 - 2x^2 + 1) $$

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

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

(C) $(6x^2 + 1)(4x^4 - 6x^2 + 1)$

(D) $(6x^2 - 1)(4x^4 + 6x^2 + 1)$

{ "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

Apply the sum of cubes formula

Combine the factored components

Answer: