what is the product?
$(x - 3)(2x^2 - 5x + 1)$

$2x^3 - x^2 + 16x + 3$
$2x^3 - 11x^2 + 16x + 3$
$2x^3 - 11x^2 + 16x - 3$
$2x^3 - x^2 + 16x - 3$

Question

what is the product?
$(x - 3)(2x^2 - 5x + 1)$

$2x^3 - x^2 + 16x + 3$
$2x^3 - 11x^2 + 16x + 3$
$2x^3 - 11x^2 + 16x - 3$
$2x^3 - x^2 + 16x - 3$

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" ], "new_concepts": [], "current_concepts": [ "Polynomial Multiplication", "Like Terms" ] } ## Distribute the linear term $$ (x - 3)(2x^2 - 5x + 1) = x(2x^2 - 5x + 1) - 3(2x^2 - 5x + 1) $$ ## Expand both parts $$ x(2x^2 - 5x + 1) = 2x^3 - 5x^2 + x $$ $$ -3(2x^2 - 5x + 1) = -6x^2 + 15x - 3 $$ ## Combine like terms $$ (2x^3 - 5x^2 + x) + (-6x^2 + 15x - 3) = 2x^3 + (-5x^2 - 6x^2) + (x + 15x) - 3 $$ $$ = 2x^3 - 11x^2 + 16x - 3 $$

(A) $2x^3 - x^2 + 16x + 3$

(B) $2x^3 - 11x^2 + 16x + 3$

(C) $2x^3 - 11x^2 + 16x - 3$

(D) $2x^3 - x^2 + 16x - 3$

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

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QUESTION IMAGE

Question

Explanation:

Distribute the linear term

Expand both parts

Combine like terms

Answer: