what must be a factor of the polynomial function $f(x)$ graphed on the coordinate plane below?

$x - 4$
$x - 2$
$x + 2$
$x + 4$

Question

what must be a factor of the polynomial function $f(x)$ graphed on the coordinate plane below?

$x - 4$
$x - 2$
$x + 2$
$x + 4$

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": [ "Factor Theorem", "Polynomial Roots" ], "new_concepts": [], "current_concepts": [ "Factor Theorem", "Polynomial Roots", "Polynomial Functions" ] } ## Identify the x-intercept from the graph Using the **Polynomial Roots** knowledge point $$ \text{The graph touches or crosses the } x\text{-axis at } x = -2. $$ ## Apply the Factor Theorem Using the **Factor Theorem** knowledge point $$ \begin{aligned} &f(-2) = 0 \ &\Rightarrow (x - (-2)) = (x + 2) \text{ is a factor of } f(x). \end{aligned} $$

$x - 4$

$x - 2$

$x + 2$

$x + 4$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Factor Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the x-intercept from the graph

Apply the Factor Theorem

Answer: