\p(x) = -2x^4 + 9x^3 + 3x^2 - 7\
\p(2) = \

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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 $x = 2$ into the polynomial $$ p(2) = -2(2)^4 + 9(2)^3 + 3(2)^2 - 7 $$ ## Simplify the exponential terms $$ \begin{aligned} 2^4 &= 16 \ 2^3 &= 8 \ 2^2 &= 4 \end{aligned} $$ ## Calculate the final value $$ \begin{aligned} p(2) &= -2(16) + 9(8) + 3(4) - 7 \ p(2) &= -32 + 72 + 12 - 7 \ p(2) &= 45 \end{aligned} $$ Given $p(x) = -2x^4 + 9x^3 + 3x^2 - 7$, then: $p(2) =$ 45 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Function Evaluation" ] }

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Question

Explanation:

Substitute \(x = 2\) into the polynomial

Simplify the exponential terms

Calculate the final value

Answer: