what is the product of $3x(x^2 + 4)$?

$x^2 + 3x + 4$
$3x^3 + 4$
$3x^3 + 12x$
$3x^2 + 12x$

Question

what is the product of $3x(x^2 + 4)$?

$x^2 + 3x + 4$
$3x^3 + 4$
$3x^3 + 12x$
$3x^2 + 12x$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Multiplication", "Distributive Property" ], "new_concepts": [], "current_concepts": [ "Polynomial Multiplication", "Distributive Property" ] } ## Apply the distributive property $$ 3x(x^2 + 4) = (3x \cdot x^2) + (3x \cdot 4) $$ ## Simplify the terms $$ 3x \cdot x^2 = 3x^3 $$ $$ 3x \cdot 4 = 12x $$ ## Combine the simplified terms $$ 3x^3 + 12x $$

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

(B) $3x^3 + 4$

(C) $3x^3 + 12x$

(D) $3x^2 + 12x$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Multiplication" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the distributive property

Simplify the terms

Combine the simplified terms

Answer: