Thank you in advance ### Synthetic Division Example1. Divide using synthetic division.\[ \frac{2x^5 - 4x^4 + 3x^3 + 4x^2 - 3x + 4}{x + 2} \]In this problem, we are given a polynomial $2x^5 - 4x^4 + 3x^3 + 4x^2 - 3x + 4$ that we need to divide by $x + 2$ using synthetic division. Here are the steps:1. **Identify the coefficients of the polynomial**: - The polynomial $2x^5 - 4x^4 + 3x^3 + 4x^2 - 3x + 4$ has these coefficients: 2, -4, 3, 4, -3, 4.2. **Write the inverse of the divisor's coefficient**: - The divisor is $x + 2$. The inverse of 2 (which comes from $x + 2 = 0$ solving to $x = -2$) is -2. 3. **Set up the synthetic division table**: - Write -2 on the left side. - Write the coefficients in a row: 2, -4, 3, 4, -3, 4.4. **Perform the synthetic division**: - Drop the first coefficient (2) straight down. - Multiply -2 by 2, and write the result under the second coefficient. - Add the second coefficient (-4) with this result (-4 + -4). - Continue the process across all coefficients.The synthetic division steps would look like this:```-2 | 2 -4 3 4 -3 4 | -4 16 -38 68 -130 ------------------------ 2 -8 19 -34 65 -126```### Explaining the Table:- **First Row**: Coefficients of the polynomial.- **Second Row**: The results from multiplying and adding each step.- **Third Row**: The coefficients of the quotient polynomial.### Quotient PolynomialThe result of the division is:\[2x^4 - 8x^3 +

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Divide using synthetic division. 2x°- 4x +3x° + 4x-3x+4 x+2 1.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 3DE

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### Synthetic Division Example

1. Divide using synthetic division.

\[ \frac{2x^5 - 4x^4 + 3x^3 + 4x^2 - 3x + 4}{x + 2} \]

In this problem, we are given a polynomial $2x^5 - 4x^4 + 3x^3 + 4x^2 - 3x + 4$ that we need to divide by $x + 2$ using synthetic division.

Here are the steps:

1. **Identify the coefficients of the polynomial**:
- The polynomial $2x^5 - 4x^4 + 3x^3 + 4x^2 - 3x + 4$ has these coefficients: 2, -4, 3, 4, -3, 4.

2. **Write the inverse of the divisor's coefficient**:
- The divisor is $x + 2$. The inverse of 2 (which comes from $x + 2 = 0$ solving to $x = -2$) is -2.

3. **Set up the synthetic division table**:
- Write -2 on the left side.
- Write the coefficients in a row: 2, -4, 3, 4, -3, 4.

4. **Perform the synthetic division**:
- Drop the first coefficient (2) straight down.
- Multiply -2 by 2, and write the result under the second coefficient.
- Add the second coefficient (-4) with this result (-4 + -4).
- Continue the process across all coefficients.

The synthetic division steps would look like this:

```
-2 | 2 -4 3 4 -3 4
| -4 16 -38 68 -130
------------------------
2 -8 19 -34 65 -126
```

### Explaining the Table:
- **First Row**: Coefficients of the polynomial.
- **Second Row**: The results from multiplying and adding each step.
- **Third Row**: The coefficients of the quotient polynomial.

### Quotient Polynomial
The result of the division is:
\[2x^4 - 8x^3 +

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