Algebra-2

To present the synthetic division of by (x - 2) in the format you've requested, here’s how it looks:

 

Synthetic Division Setup

When dividing by (x - 2):

The zero used is 2 (because x - 2 = 0 gives x = 2).

The coefficients of the polynomial are (3, -2, 1, 4).

 

Synthetic Division Representation

Here’s the synthetic division setup and the steps:

  2  |   3   -2    1    4

     |         6     8   18

     |---------------------

         3     4    9   22

 

Explanation of the Steps:

1.Start with the leading coefficient: Bring down the 3.

2.Multiply 3 by 2 (the zero) to get 6 and write it under -2.

3.Add -2 + 6 to get 4.

4.Multiply 4 by 2 to get 8 and write it under 1.

5.Add 1 + 8 to get 9.

6.Multiply 9 by 2 to get 18 and write it under 4.

7.Add 4 + 18 to get 22.

 

Final Interpretation

The bottom row, (3, 4, 9), represents the coefficients of the quotient polynomial, and 22 is the remainder:

The quotient is

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