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

if $x + 2$ is a factor of $x^3 - 6x^2 - 11x + k$, then $k =$

Question

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

if $x + 2$ is a factor of $x^3 - 6x^2 - 11x + k$, then $k =$

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 $$ \begin{aligned} &P(x) = x^3 - 6x^2 - 11x + k \ &P(-2) = 0 \end{aligned} $$ ## Substitute and solve for k $$ \begin{aligned} &(-2)^3 - 6(-2)^2 - 11(-2) + k = 0 \ &-8 - 6(4) + 22 + k = 0 \ &-8 - 24 + 22 + k = 0 \ &-10 + k = 0 \ &k = 10 \end{aligned} $$ If $x + 2$ is a factor of $x^3 - 6x^2 - 11x + k$, then $k =$ 10. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factor Theorem" ] }

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Question

Explanation:

Apply the Factor Theorem

Substitute and solve for k

Answer: