Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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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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Transcribed Image Text:**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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