multiply.
$(2x^2 + 4x - 3)(x^2 - 2x + 5)$

$2x^4 + 7x^2 - 15$
$2x^4 - 8x^2 - 15$
$2x^4 - x^2 + 26x - 15$
$2x^4 + 8x^3 - x^2 + 26x - 15$

Question

multiply.
$(2x^2 + 4x - 3)(x^2 - 2x + 5)$

$2x^4 + 7x^2 - 15$
$2x^4 - 8x^2 - 15$
$2x^4 - x^2 + 26x - 15$
$2x^4 + 8x^3 - x^2 + 26x - 15$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Multiplying Polynomials", "Distributive Property" ], "new_concepts": [], "current_concepts": [ "Multiplying Polynomials", "Distributive Property" ] } ## Distribute each term of the first trinomial $$ \begin{aligned} (2x^2 + 4x - 3)(x^2 - 2x + 5) = &2x^2(x^2 - 2x + 5) \ &+ 4x(x^2 - 2x + 5) \ &- 3(x^2 - 2x + 5) \end{aligned} $$ ## Expand the individual products $$ \begin{aligned} 2x^2(x^2 - 2x + 5) &= 2x^4 - 4x^3 + 10x^2 \ 4x(x^2 - 2x + 5) &= 4x^3 - 8x^2 + 20x \ -3(x^2 - 2x + 5) &= -3x^2 + 6x - 15 \end{aligned} $$ ## Combine like terms $$ \begin{aligned} \text{Sum} = &2x^4 + (-4x^3 + 4x^3) + (10x^2 - 8x^2 - 3x^2) + (20x + 6x) - 15 \ = &2x^4 + 0x^3 - x^2 + 26x - 15 \ = &2x^4 - x^2 + 26x - 15 \end{aligned} $$

(A) $2x^4 + 7x^2 - 15$

(B) $2x^4 - 8x^2 - 15$

(C) $2x^4 - x^2 + 26x - 15$

(D) $2x^4 + 8x^3 - x^2 + 26x - 15$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Multiplying Polynomials" ] }

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QUESTION IMAGE

Question

Explanation:

Distribute each term of the first trinomial

Expand the individual products

Combine like terms

Answer: