if $(x - 2k)$ is a factor of $f(x)$, which of the following must be true?

$f(2k) = 0$
$f(-2k) = 0$
a root of $f(x)$ is $x = -2k$
a $y$ intercept of $f(x)$ is $x = 2k$

Question

if $(x - 2k)$ is a factor of $f(x)$, which of the following must be true?

$f(2k) = 0$
$f(-2k) = 0$
a root of $f(x)$ is $x = -2k$
a $y$ intercept of $f(x)$ is $x = 2k$

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" ], "new_concepts": [], "current_concepts": [ "Factor Theorem", "Polynomial Roots" ] } ## Apply the Factor Theorem Using the *Factor Theorem* knowledge point $$ \text{If } (x - c) \text{ is a factor of } f(x), \text{ then } f(c) = 0. $$ ## Substitute the given factor Using the *Factor Theorem* knowledge point $$ \begin{aligned} &\text{Given factor: } (x - 2k) \implies c = 2k\ &f(2k) = 0 \end{aligned} $$

(A) $f(2k) = 0$

(B) $f(-2k) = 0$

(C) A root of $f(x)$ is $x = -2k$

(D) A $y$-intercept of $f(x)$ is $x = 2k$

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

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Question

Explanation:

Apply the Factor Theorem

Substitute the given factor

Answer: