multiplication of polynomials
what is the product?
$(3x - 6)(2x^2 - 7x + 1)$

- $-12x^2 + 21x + 6$
- $6x^3 - 27x^2 - 39x + 6$
- $-12x^2 + 42x - 6$
- $6x^3 - 33x^2 + 45x - 6$

Question

multiplication of polynomials
what is the product?
$(3x - 6)(2x^2 - 7x + 1)$

- $-12x^2 + 21x + 6$
- $6x^3 - 27x^2 - 39x + 6$
- $-12x^2 + 42x - 6$
- $6x^3 - 33x^2 + 45x - 6$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Polynomial Multiplication", "Distributive Property" ], "current_concepts": [ "Polynomial Multiplication", "Distributive Property" ] } ## Distribute the terms of the binomial $$ (3x - 6)(2x^2 - 7x + 1) = 3x(2x^2 - 7x + 1) - 6(2x^2 - 7x + 1) $$ ## Expand each distributed term $$ \begin{aligned} 3x(2x^2 - 7x + 1) &= 6x^3 - 21x^2 + 3x \ -6(2x^2 - 7x + 1) &= -12x^2 + 42x - 6 \end{aligned} $$ ## Combine like terms $$ \begin{aligned} (6x^3 - 21x^2 + 3x) + (-12x^2 + 42x - 6) &= 6x^3 + (-21x^2 - 12x^2) + (3x + 42x) - 6 \ &= 6x^3 - 33x^2 + 45x - 6 \end{aligned} $$

(A) $-12x^2 + 21x + 6$

(B) $6x^3 - 27x^2 - 39x + 6$

(C) $-12x^2 + 42x - 6$

(D) $6x^3 - 33x^2 + 45x - 6$

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

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Question

Explanation:

Distribute the terms of the binomial

Expand each distributed term

Combine like terms

Answer: