type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.

if $p - 1$ is a factor of $p^4 + p^2 + p - k$, the value of $k$ is .

Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.

if $p - 1$ is a factor of $p^4 + p^2 + p - k$, the value of $k$ is  .

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factor Theorem" ], "new_concepts": [], "current_concepts": [ "Factor Theorem", "Polynomial Factoring" ] } ## Apply the Factor Theorem $$ \begin{aligned} &f(p) = p^4 + p^2 + p - k \ &f(1) = 0 \end{aligned} $$ ## Solve for k $$ \begin{aligned} &1^4 + 1^2 + 1 - k = 0 \ &1 + 1 + 1 - k = 0 \ &3 - k = 0 \ &k = 3 \end{aligned} $$ If $p - 1$ is a factor of $p^4 + p^2 + p - k$, the value of $k$ is 3. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factor Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Apply the Factor Theorem

Solve for k

Answer: