divide using synthetic division.

\frac{11x^2 + 59x - 42}{x + 6}

a. x - 7
b. -7x + 6
c. 11x - 7
d. -11x + 7

Question

divide using synthetic division.

\frac{11x^2 + 59x - 42}{x + 6}

a. x - 7
b. -7x + 6
c. 11x - 7
d. -11x + 7

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Synthetic Division" ], "new_concepts": [], "current_concepts": [ "Synthetic Division", "Polynomial Long Division" ] } ## Identify the divisor and dividend Using the *Synthetic Division* knowledge point $$ \begin{aligned} &\text{Dividend: } 11x^2 + 59x - 42\ &\text{Divisor: } x + 6 \implies c = -6\ &\text{Coefficients: } [11, 59, -42] \end{aligned} $$ ## Set up and perform synthetic division Using the *Synthetic Division* knowledge point $$ \begin{array}{r|rrr} -6 & 11 & 59 & -42 \ & & -66 & 42 \ \hline & 11 & -7 & 0 \end{array} $$ ## Interpret the quotient and remainder Using the *Synthetic Division* knowledge point $$ \begin{aligned} &\text{Quotient coefficients: } [11, -7]\ &\text{Remainder: } 0\ &\text{Result: } 11x - 7 \end{aligned} $$

A. $x - 7$

B. $-7x + 6$

C. $11x - 7$

D. $-11x + 7$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Synthetic Division" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the divisor and dividend

Set up and perform synthetic division

Interpret the quotient and remainder

Answer: