consider the function $f(x) = (x - 3)^2(x + 2)^2(x - 1)$.

the zero has a multiplicity of 1.

the zero -2 has a multiplicity of .

Question

consider the function $f(x) = (x - 3)^2(x + 2)^2(x - 1)$.

the zero   has a multiplicity of 1.

the zero -2 has a multiplicity of  .

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Root Multiplicity", "Factored Polynomials" ], "new_concepts": [], "current_concepts": [ "Root Multiplicity", "Factored Polynomials" ] } ## Identify the zeros and their corresponding exponents $$ \begin{aligned} &f(x) = (x - 3)^2(x + 2)^2(x - 1)^1 \ &\text{Factor } (x - 3)^2 \implies \text{Zero: } 3, \text{ Multiplicity: } 2 \ &\text{Factor } (x + 2)^2 \implies \text{Zero: } -2, \text{ Multiplicity: } 2 \ &\text{Factor } (x - 1)^1 \implies \text{Zero: } 1, \text{ Multiplicity: } 1 \end{aligned} $$ ## Match the zeros to the given blanks $$ \begin{aligned} &\text{The zero with multiplicity of 1 is } 1. \ &\text{The zero } -2 \text{ has a multiplicity of } 2. \end{aligned} $$ Consider the function $f(x) = (x - 3)^2(x + 2)^2(x - 1)$. ## Question 1 The zero 1 has a multiplicity of 1. ## Question 2 The zero -2 has a multiplicity of 2. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Root Multiplicity" ] }

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Question

Explanation:

Identify the zeros and their corresponding exponents

Match the zeros to the given blanks

Answer:

Question 1

Question 2