thank you so much for answering ### Synthetic Division Example#### Problem:Divide using synthetic division.\[ \frac{2x^5 - 4x^4 + 3x^3 + 4x^2 - 3x + 4}{x + 2} \]---To solve this polynomial division problem using synthetic division, follow these steps:1. **Write down the coefficients of the dividend polynomial**: \( 2, -4, 3, 4, -3, 4 \).2. **Identify the zero of the divisor** \( x + 2 \): The zero is \(-2\).3. **Set up the synthetic division table**: Place \(-2\) on the left, and all coefficients of the dividend in a row.Here’s a detailed step-by-step process to perform synthetic division with this setup:\[\begin{array}{r|rrrrrr} -2 & 2 & -4 & 3 & 4 & -3 & 4 \\\hline & & -4 & 12 & -30 & 68 & -142 \\\hline & 2 & -8 & 11 & -22 & 44 & -138 \\\end{array}\]- **Step 1**: Bring down the first coefficient \(2\) directly under the line.- **Step 2**: Multiply \(2\) by \(-2\) (the zero of the divisor) to get \(-4\), then write it under the next coefficient \(-4\).- **Step 3**: Add \(-4\) and \(-4\) to get \(-8\).- **Step 4**: Multiply \(-8\) by \(-2\) to get \(16\), then place it under the next coefficient \(3\).- **Step 5**: Add \(3\) and \(16\) to get \(11\).- **Step 6**: Continue this process until the last coefficient is processed.The final row \(2, -8, 11, -22, 44, -138\) represents the coefficients of the quotient polynomial and the remainder. Hence, the quotient from synthetic division is: \[ 2x^4 - 8x^3 + 11x^2 - 22x +

Name: thank you so much for answering ### Synthetic Division Example#### Pro
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: thank you so much for answering ### Synthetic Division Example#### Problem:Divide using synthetic division.\[ \frac{2x^5 - 4x^4 + 3x^3 + 4x^2 - 3x + 4}{x + 2} \]---To solve this polynomial division problem using synthetic division, follow these steps