consider the division of (3b^2 + 9b + 4) by (3b).

\\frac{3b^2 + 9b + 4}{3b}\
\= \frac{3b^2}{3b} + \frac{9b}{3b} + \frac{4}{3b}\
\= b + x + \frac{4}{3b}\

what is the value of (x)?

Question

consider the division of (3b^2 + 9b + 4) by (3b).

\\frac{3b^2 + 9b + 4}{3b}\
\= \frac{3b^2}{3b} + \frac{9b}{3b} + \frac{4}{3b}\
\= b + x + \frac{4}{3b}\

what is the value of (x)?

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": [ "Division with Remainders" ], "new_concepts": [ "Polynomial Division by Monomial" ], "current_concepts": [ "Division with Remainders", "Polynomial Division by Monomial" ] } ## Identify the term corresponding to $X$ Using the *Division with Remainders* knowledge point $$ \frac{3b^2+9b+4}{3b} = \frac{3b^2}{3b} + \frac{9b}{3b} + \frac{4}{3b} $$ ## Simplify the middle term to find $X$ Using the *Division with Remainders* knowledge point $$ \begin{aligned} &\frac{3b^2}{3b} = b\ &X = \frac{9b}{3b} = 3\ &\frac{4}{3b} = \frac{4}{3b} \end{aligned} $$ ## Match with the given options Using the *Division with Remainders* knowledge point $$ X = 3 $$

(A) $\frac{1}{27b}$

(B) 27

(C) 3

(D) $\frac{1}{3b}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Division by Monomial" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the term corresponding to \(X\)

Simplify the middle term to find \(X\)

Match with the given options

Answer: