Algebra-2

To divide the polynomial by (x - 1) using synthetic division, we will follow these steps:

Step 1: Set Up Synthetic Division

Identify the coefficients of the polynomial:

Thus, the coefficients are:

5, -2, 3, 0, -1, 1

 

Use 1 (from x - 1) for synthetic division.

 

Step 2: Perform Synthetic Division

Set up the synthetic division as follows:

   1 |  5  -2   3   0  -1   1

     |        5   3   6   6   5

     -------------------------

         5   3   6   6   5   6

  

Step-by-Step Calculation:

Bring down the first coefficient 5:

The result so far is 5

 

Multiply 1 (the divisor root) by 5:

Write 5 under the next coefficient -2

 

Add the values in the second column:

-2 + 5 = 3

Write 3 in the result row.

 

Multiply 1 by 3:

Write 3 under the next coefficient 3

 

Add the values in the third column:

3 + 3 = 6

Write 6 in the result row.

 

Multiply 1 by 6:

Write 6 under the next coefficient 0

Add the values in the fourth column:

0 + 6 = 6

Write 6 in the result row.

 

Multiply 1 by 6:

Write 6 under the next coefficient -1

 

Add the values in the last column:

-1 + 6 = 5

Write 5 in the result row.

 

Multiply 1 by 5:

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