divide the following polynomials.

\\frac{6x^2 - 7x + 10}{3x - 2}\

\?x + \quad + \frac{\quad}{3x - 2}\

Question

divide the following polynomials.

\\frac{6x^2 - 7x + 10}{3x - 2}\

\?x + \quad + \frac{\quad}{3x - 2}\

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": [ "Polynomial Long Division" ], "new_concepts": [], "current_concepts": [ "Polynomial Long Division", "Synthetic Division" ] } ## Divide the leading terms Using the *Polynomial Long Division* knowledge point $$ \frac{6x^2}{3x} = 2x $$ ## Multiply and subtract the first term Using the *Polynomial Long Division* knowledge point $$ \begin{aligned} &2x(3x - 2) = 6x^2 - 4x\ &(6x^2 - 7x + 10) - (6x^2 - 4x) = -3x + 10 \end{aligned} $$ ## Divide the remaining leading terms Using the *Polynomial Long Division* knowledge point $$ \frac{-3x}{3x} = -1 $$ ## Multiply and subtract the second term Using the *Polynomial Long Division* knowledge point $$ \begin{aligned} &-1(3x - 2) = -3x + 2\ &(-3x + 10) - (-3x + 2) = 8 \end{aligned} $$ ## Write the final quotient and remainder Using the *Polynomial Long Division* knowledge point $$ \frac{6x^2 - 7x + 10}{3x - 2} = 2x - 1 + \frac{8}{3x - 2} $$ Divide the following polynomials. $$ \frac{6x^2 - 7x + 10}{3x - 2} $$ 2$x +$ $-1$ $+$ $\frac{8}{3x - 2}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Long Division" ] }

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QUESTION IMAGE

Question

Explanation:

Divide the leading terms

Multiply and subtract the first term

Divide the remaining leading terms

Multiply and subtract the second term

Write the final quotient and remainder

Answer: