factor the following expression: $7x^3 + 28x^2 + 21x$

a $x(7x + 14x + 21)$

b $7(x^3 + 2x^2 + 3)$

c $7x(x^2 + 2x + 3)$

d $7x(x + 3)(x + 1)$

Question

factor the following expression: $7x^3 + 28x^2 + 21x$

a $x(7x + 14x + 21)$

b $7(x^3 + 2x^2 + 3)$

c $7x(x^2 + 2x + 3)$

d $7x(x + 3)(x + 1)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring Trinomials", "Quadratic Factoring" ], "new_concepts": [ "Greatest Common Factor Factoring" ], "current_concepts": [ "Greatest Common Factor Factoring", "Factoring Trinomials", "Quadratic Factoring" ] } ## Factor out the greatest common factor $$ 7x^3 + 28x^2 + 21x = 7x(x^2 + 4x + 3) $$ ## Factor the remaining quadratic trinomial $$ x^2 + 4x + 3 = (x + 3)(x + 1) $$ ## Combine the factored components $$ 7x(x + 3)(x + 1) $$

(A) $x(7x + 14x + 21)$

(B) $7(x^3 + 2x^2 + 3)$

(C) $7x(x^2 + 2x + 3)$

(D) $7x(x + 3)(x + 1)$

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

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QUESTION IMAGE

Question

Explanation:

Factor out the greatest common factor

Factor the remaining quadratic trinomial

Combine the factored components

Answer: