divide using synthetic division.

$(5x^3 - 3x^2 + 5x - 1) \div (x - 1)$

$(5x^3 - 3x^2 + 5x - 1) \div (x - 1) = $
(simplify your answer. do not factor.)

Question

divide using synthetic division.

$(5x^3 - 3x^2 + 5x - 1) \div (x - 1)$

$(5x^3 - 3x^2 + 5x - 1) \div (x - 1) = $
(simplify your answer. do not factor.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Synthetic Division" ], "new_concepts": [], "current_concepts": [ "Synthetic Division", "Polynomial Long Division", "Division Algorithm" ] } ## Identify the setup for synthetic division Using the **Synthetic Division** knowledge point $$ \begin{aligned} &\text{Dividend: } 5x^3 - 3x^2 + 5x - 1 \implies \text{Coefficients: } [5, -3, 5, -1]\ &\text{Divisor: } x - 1 \implies c = 1 \end{aligned} $$ ## Perform synthetic division calculations Using the **Synthetic Division** knowledge point $$ \begin{array}{c|rrrr} 1 & 5 & -3 & 5 & -1 \ & & 5 & 2 & 7 \ \hline & 5 & 2 & 7 & \underline{6} \end{array} $$ ## Interpret the quotient and remainder Using the **Synthetic Division** knowledge point $$ \begin{aligned} &\text{Quotient: } 5x^2 + 2x + 7\ &\text{Remainder: } 6\ &\text{Result: } 5x^2 + 2x + 7 + \frac{6}{x-1} \end{aligned} $$ Divide using synthetic division. $$(5x^3 - 3x^2 + 5x - 1) \div (x - 1) =$$ $5x^2 + 2x + 7 + \frac{6}{x-1}$ (Simplify your answer. Do not factor.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Synthetic Division" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the setup for synthetic division

Perform synthetic division calculations

Interpret the quotient and remainder

Answer: