use synthetic division and the remainder theorem to find the indicated function value.

$f(x) = x^4 - 5x^3 - 5x^2 - 3x - 3$; $f(-3)$

a. 96
b. -177
c. -531
d. 177

Question

use synthetic division and the remainder theorem to find the indicated function value.

$f(x) = x^4 - 5x^3 - 5x^2 - 3x - 3$; $f(-3)$

a. 96
b. -177
c. -531
d. 177

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Synthetic Division" ], "new_concepts": [ "Remainder Theorem" ], "current_concepts": [ "Synthetic Division", "Remainder Theorem" ] } ## State the given values and theorem Using the *Synthetic Division* knowledge point $$ \begin{aligned} &f(x) = x^4 - 5x^3 - 5x^2 - 3x - 3\ &c = -3\ &\text{Remainder Theorem: } f(c) = R \end{aligned} $$ ## Set up the synthetic division table Using the *Synthetic Division* knowledge point $$ \begin{array}{r|rrrrr} -3 & 1 & -5 & -5 & -3 & -3 \ & & & & & \ \hline & & & & & \end{array} $$ ## Perform the synthetic division steps Using the *Synthetic Division* knowledge point $$ \begin{array}{r|rrrrr} -3 & 1 & -5 & -5 & -3 & -3 \ & & -3 & 24 & -57 & 180 \ \hline & 1 & -8 & 19 & -60 & 177 \end{array} $$ ## Identify the remainder and function value Using the *Synthetic Division* knowledge point $$ \begin{aligned} &R = 177\ &f(-3) = 177 \end{aligned} $$

A. 96

B. -177

C. -531

D. 177

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Remainder Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

State the given values and theorem

Set up the synthetic division table

Perform the synthetic division steps

Identify the remainder and function value

Answer: