the following function is given.

\f(x) = x^3 - 3x^2 - 4x + 12\

a. list all rational zeros that are possible according to the rational zero theorem.

(use a comma to separate answers as needed.)

Question

the following function is given.

\f(x) = x^3 - 3x^2 - 4x + 12\

a. list all rational zeros that are possible according to the rational zero theorem.

(use a comma to separate answers as needed.)

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": [ "Rational Root Theorem" ], "new_concepts": [], "current_concepts": [ "Rational Root Theorem", "Polynomial Functions" ] } ## Identify the coefficients of the polynomial Using the *Rational Root Theorem* knowledge point $$ \begin{aligned} &f(x) = x^3 - 3x^2 - 4x + 12\ &\text{Leading coefficient } a_n = 1\ &\text{Constant term } a_0 = 12 \end{aligned} $$ ## Find the factors of the constant term and leading coefficient Using the *Rational Root Theorem* knowledge point $$ \begin{aligned} &\text{Factors of } a_0 = 12 \quad (p): \pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12\ &\text{Factors of } a_n = 1 \quad (q): \pm 1 \end{aligned} $$ ## List all possible rational zeros Using the *Rational Root Theorem* knowledge point $$ \begin{aligned} &\frac{p}{q} = \frac{\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12}{\pm 1}\ &\frac{p}{q} = 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12 \end{aligned} $$ a. List all rational zeros that are possible according to the Rational Zero Theorem. $1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12$ (Use a comma to separate answers as needed.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Rational Root Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients of the polynomial

Find the factors of the constant term and leading coefficient

List all possible rational zeros

Answer: