enter the correct answer in the box.

what is the standard form polynomial that represents this product?

$(-2m^3 + 3m^2 - m)(4m^2 + m - 5)$

Question

enter the correct answer in the box.

what is the standard form polynomial that represents this product?

$(-2m^3 + 3m^2 - m)(4m^2 + m - 5)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Operations" ], "new_concepts": [], "current_concepts": [ "Polynomial Operations", "Factoring Polynomials" ] } ## Multiply the polynomials term-by-term $$ \begin{aligned} (-2m^3 + 3m^2 - m)(4m^2 + m - 5) = & -2m^3(4m^2 + m - 5) \ & + 3m^2(4m^2 + m - 5) \ & - m(4m^2 + m - 5) \end{aligned} $$ ## Expand each term $$ \begin{aligned} -2m^3(4m^2 + m - 5) &= -8m^5 - 2m^4 + 10m^3 \ 3m^2(4m^2 + m - 5) &= 12m^4 + 3m^3 - 15m^2 \ -m(4m^2 + m - 5) &= -4m^3 - m^2 + 5m \end{aligned} $$ ## Combine like terms $$ \begin{aligned} \text{Product} = & -8m^5 \ & + (-2 + 12)m^4 \ & + (10 + 3 - 4)m^3 \ & + (-15 - 1)m^2 \ & + 5m \ = & -8m^5 + 10m^4 + 9m^3 - 16m^2 + 5m \end{aligned} $$ What is the standard form polynomial that represents this product? $(-2m^3 + 3m^2 - m)(4m^2 + m - 5) =$ $-8m^5 + 10m^4 + 9m^3 - 16m^2 + 5m$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Operations" ] }

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QUESTION IMAGE

Question

Explanation:

Multiply the polynomials term-by-term

Expand each term

Combine like terms

Answer: