divide.

\(4x^3 + 4x^2 + 3x + 10) \div (2x + 1)\

your answer should give the quotient and the remainder.

quotient:
remainder:

Question

divide.

\(4x^3 + 4x^2 + 3x + 10) \div (2x + 1)\

your answer should give the quotient and the remainder.

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": [ "Algebraic Expressions" ], "new_concepts": [ "Polynomial Long Division", "Quotient and Remainder" ], "current_concepts": [ "Algebraic Expressions", "Polynomial Long Division", "Quotient and Remainder" ] } ## Set up polynomial long division $$ (4x^3 + 4x^2 + 3x + 10) \div (2x + 1) $$ ## Perform division steps $$ \begin{array}{r|l} \text{Step 1:} & \frac{4x^3}{2x} = 2x^2 \ \text{Subtract:} & (4x^3 + 4x^2 + 3x + 10) - 2x^2(2x + 1) = 2x^2 + 3x + 10 \ \text{Step 2:} & \frac{2x^2}{2x} = x \ \text{Subtract:} & (2x^2 + 3x + 10) - x(2x + 1) = 2x + 10 \ \text{Step 3:} & \frac{2x}{2x} = 1 \ \text{Subtract:} & (2x + 10) - 1(2x + 1) = 9 \end{array} $$ ## Identify quotient and remainder $$ \begin{aligned} \text{Quotient} &= 2x^2 + x + 1 \ \text{Remainder} &= 9 \end{aligned} $$ Divide. $$(4x^3 + 4x^2 + 3x + 10) \div (2x + 1)$$ Your answer should give the quotient and the remainder. Quotient: $2x^2 + x + 1$ Remainder: 9 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Long Division" ] }

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QUESTION IMAGE

Question

Explanation:

Set up polynomial long division

Perform division steps

Identify quotient and remainder

Answer: