Hi, need a step by step break down please **Problem 1:**Use synthetic division and the Remainder Theorem to evaluate $ f(9) $ for $ f(x) = 6x^3 - 8x^2 + 4x - 3 $.**Solution:**Apply synthetic division to find the value of the function at $ x = 9 $.**Remainder Theorem Explanation:**The Remainder Theorem states that if a polynomial $ f(x) $ is divided by $ x - c $, then the remainder of this division is $ f(c) $.**Synthetic Division Steps:**1. Write down the coefficients of the polynomial: $ 6, -8, 4, -3 $.2. Use $ x = 9 $ for the division process.3. Set up the synthetic division process: - Bring down the leading coefficient. - Multiply by 9 and add to the next coefficient, repeating for each subsequent coefficient.After completing the synthetic division, the remainder gives the value of $ f(9) $.**Final Answer:**$ \text{Ans 1 } f(9) = \underline{\hspace{5cm}} $Complete the calculations to fill in the answer.

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Answered: Use synthetic division and the…

Math

Calculus

Use synthetic division and the Remainder Theorem to evaluate f(9) for f(x)= 6x³ – 8x² +4x – 3. 1.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Hi, need a step by step break down please

**Problem 1:**

Use synthetic division and the Remainder Theorem to evaluate $ f(9) $ for $ f(x) = 6x^3 - 8x^2 + 4x - 3 $.

**Solution:**

Apply synthetic division to find the value of the function at $ x = 9 $.

**Remainder Theorem Explanation:**

The Remainder Theorem states that if a polynomial $ f(x) $ is divided by $ x - c $, then the remainder of this division is $ f(c) $.

**Synthetic Division Steps:**

1. Write down the coefficients of the polynomial: $ 6, -8, 4, -3 $.
2. Use $ x = 9 $ for the division process.
3. Set up the synthetic division process:
- Bring down the leading coefficient.
- Multiply by 9 and add to the next coefficient, repeating for each subsequent coefficient.

After completing the synthetic division, the remainder gives the value of $ f(9) $.

**Final Answer:**

$ \text{Ans 1 } f(9) = \underline{\hspace{5cm}} $

Complete the calculations to fill in the answer.

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