let $f(n) = 2n^5 - 7n^3 - 12$. find $f(4)$ either by using synthetic division and the remainder theorem, or by evaluating $f(4)$ directly.

$f(4) =$

Question

let $f(n) = 2n^5 - 7n^3 - 12$. find $f(4)$ either by using synthetic division and the remainder theorem, or by evaluating $f(4)$ directly.

$f(4) =$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Remainder Theorem" ], "new_concepts": [], "current_concepts": [ "Remainder Theorem", "Synthetic Division" ] } ## Evaluate the function directly at n = 4 $$ \begin{aligned} f(4) &= 2(4)^5 - 7(4)^3 - 12 \ &= 2(1024) - 7(64) - 12 \ &= 2048 - 448 - 12 \ &= 1588 \end{aligned} $$ ## Verify using synthetic division $$ \begin{array}{r|cccccc} 4 & 2 & 0 & -7 & 0 & 0 & -12 \ & & 8 & 32 & 100 & 400 & 1600 \ \hline & 2 & 8 & 25 & 100 & 400 & 1588 \end{array} $$ Let $f(n) = 2n^5 - 7n^3 - 12$. Find $f(4)$ either by using synthetic division and the Remainder Theorem, or by evaluating $f(4)$ directly. $f(4) =$ 1588 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Remainder Theorem" ] }

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Question

Explanation:

Evaluate the function directly at n = 4

Verify using synthetic division

Answer: