determine the quotient and remainder.

\(5x^3 + 2x - 3) \div (x - 2)\

quotient

remainder

Question

determine the quotient and remainder.

\(5x^3 + 2x - 3) \div (x - 2)\

quotient

remainder

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Polynomial Division", "Synthetic Division", "Remainder Theorem" ], "current_concepts": [ "Polynomial Division", "Synthetic Division", "Remainder Theorem" ] } ## Set up synthetic division $$ \begin{array}{r|rrrr} 2 & 5 & 0 & 2 & -3 \ & & 10 & 20 & 44 \ \hline & 5 & 10 & 22 & 41 \end{array} $$ ## Identify quotient and remainder $$ \begin{aligned} \text{Quotient} &= 5x^2 + 10x + 22 \ \text{Remainder} &= 41 \end{aligned} $$ Determine the quotient and remainder. $$(5x^3 + 2x - 3) \div (x - 2)$$ Quotient: $5x^2 + 10x + 22$ Remainder: 41 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Division" ] }

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QUESTION IMAGE

Question

Explanation:

Set up synthetic division

Identify quotient and remainder

Answer: