We appreciate your visit to What is the remainder in the synthetic division problem below tex begin array c ccc 1 1 2 3 hline end array tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Sure! Let's go through the process of synthetic division to find the remainder.
### Synthetic Division Steps:
1. Identify the Divisor:
- In synthetic division, the divisor is usually in the form [tex]\( x - c \)[/tex]. Here, we've assumed the divisor is [tex]\( x - 1 \)[/tex], which means [tex]\( c = 1 \)[/tex].
2. Set Up Coefficients:
- Write down the coefficients of the dividend polynomial. In this case, the coefficients are 1, 2, and -3.
3. Perform Synthetic Division:
- Start by bringing down the leading coefficient (which is 1) to the bottom row.
- Multiply this number by the divisor root ([tex]\( c=1 \)[/tex]) and write the result under the next coefficient.
- Add the current column and write the result below the line.
- Repeat the multiply and add steps for the remaining coefficients.
4. Determine the Remainder:
- The last number at the bottom is the remainder.
### Work Through the Example:
- Coefficients: [tex]\( [1, 2, -3] \)[/tex]
#### Step-by-Step Process:
- Step 1: Bring down the 1 (the leading coefficient).
- New row: [tex]\([1]\)[/tex]
- Step 2: Multiply 1 (brought down) by 1 (the root of the divisor) and add to the next coefficient (2).
- Calculation: [tex]\( 1 \times 1 + 2 = 3 \)[/tex]
- Update row: [tex]\([1, 3]\)[/tex]
- Step 3: Multiply 3 by 1 (the root of the divisor) and add to the next coefficient (-3).
- Calculation: [tex]\( 3 \times 1 + (-3) = 0 \)[/tex]
- Update row: [tex]\([1, 3, 0]\)[/tex]
- Remainder: The last value in the row is 0.
Therefore, the remainder in the synthetic division is 0.
### Synthetic Division Steps:
1. Identify the Divisor:
- In synthetic division, the divisor is usually in the form [tex]\( x - c \)[/tex]. Here, we've assumed the divisor is [tex]\( x - 1 \)[/tex], which means [tex]\( c = 1 \)[/tex].
2. Set Up Coefficients:
- Write down the coefficients of the dividend polynomial. In this case, the coefficients are 1, 2, and -3.
3. Perform Synthetic Division:
- Start by bringing down the leading coefficient (which is 1) to the bottom row.
- Multiply this number by the divisor root ([tex]\( c=1 \)[/tex]) and write the result under the next coefficient.
- Add the current column and write the result below the line.
- Repeat the multiply and add steps for the remaining coefficients.
4. Determine the Remainder:
- The last number at the bottom is the remainder.
### Work Through the Example:
- Coefficients: [tex]\( [1, 2, -3] \)[/tex]
#### Step-by-Step Process:
- Step 1: Bring down the 1 (the leading coefficient).
- New row: [tex]\([1]\)[/tex]
- Step 2: Multiply 1 (brought down) by 1 (the root of the divisor) and add to the next coefficient (2).
- Calculation: [tex]\( 1 \times 1 + 2 = 3 \)[/tex]
- Update row: [tex]\([1, 3]\)[/tex]
- Step 3: Multiply 3 by 1 (the root of the divisor) and add to the next coefficient (-3).
- Calculation: [tex]\( 3 \times 1 + (-3) = 0 \)[/tex]
- Update row: [tex]\([1, 3, 0]\)[/tex]
- Remainder: The last value in the row is 0.
Therefore, the remainder in the synthetic division is 0.
Thanks for taking the time to read What is the remainder in the synthetic division problem below tex begin array c ccc 1 1 2 3 hline end array tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
