what is the exponent?

(y = (x + 4)(x + 3)^2(x + 1)^{?})

3
1
2

Question

what is the exponent?

(y = (x + 4)(x + 3)^2(x + 1)^{?})

3
1
2

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": [ "Polynomial Multiplicity", "Graph Behavior at Roots" ], "new_concepts": [], "current_concepts": [ "Polynomial Multiplicity", "Graph Behavior at Roots" ] } ## Identify the target root and behavior Using the *Graph Behavior at Roots* and *Polynomial Multiplicity* knowledge points $$ \begin{aligned} &\text{Target factor: } (x+1)^{[?]} \implies \text{Root at } x = -1\ &\text{Graph behavior at } x = -1 \text{ (circled in red): inflection point (crosses while flattening)}\ &\text{Multiplicity of an inflection-crossing root must be odd and greater than 1} \implies [?] = 3 \end{aligned} $$

(A) 3

(B) 1

(C) 2

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Multiplicity" ] }

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Question

Explanation:

Identify the target root and behavior

Answer: