given the following function, find $p(-2)$.
\p(x) = 3x^4 - 3x^3 + 3x^2 + 6\

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Evaluation" ], "new_concepts": [], "current_concepts": [ "Function Evaluation", "Polynomial Evaluation" ] } ## Substitute the value into the function $$ p(-2) = 3(-2)^4 - 3(-2)^3 + 3(-2)^2 + 6 $$ ## Simplify the exponential terms $$ \begin{aligned} (-2)^4 &= 16 \ (-2)^3 &= -8 \ (-2)^2 &= 4 \end{aligned} $$ ## Calculate the final value $$ \begin{aligned} p(-2) &= 3(16) - 3(-8) + 3(4) + 6 \ p(-2) &= 48 + 24 + 12 + 6 \ p(-2) &= 90 \end{aligned} $$ Given the following function, find $p(-2)$. $$p(x) = 3x^4 - 3x^3 + 3x^2 + 6$$ $p(-2) =$ 90 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Function Evaluation" ] }

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Explanation:

Substitute the value into the function

Simplify the exponential terms

Calculate the final value

Answer: