Algebra-2

To divide the polynomial () by (x + 2) using synthetic division, follow these steps:

 

Step 1: Set Up Synthetic Division

Identify the zero: Since we are dividing by (x + 2), we use -2 (the value that makes x + 2 = 0).

List the coefficients: Write down the coefficients of the polynomial :

Coefficients: (5, 4, 3)

 

Step 2: Perform Synthetic Division

Set up the synthetic division:

-2 |  5    4     3

   |       -10   12

   |-----------------

       5    -6    15

 

Step 3: Carry Out the Division

Bring down the leading coefficient 5:

-2 |  5   4   3

   |      

   |-----------------

     5  

 

 

Multiply 5 (the number we brought down) by -2 (the zero) to get -10.

Add this -10 to 4:

4 + (-10) = -6

 

Update the table:

-2 |  5   4   3

   |      -10

   |-----------------

       5  -6  

 

Repeat the process:

Multiply -6 by -2 to get 12.

Add this 12 to 3:

3 + 12 = 15

 

Final update:

-2 |  5    4    3

   |      -10   12

   |-----------------

      5    -6   15

 

Step 4: Interpret the Result

The bottom row shows the coefficients of the quotient polynomial:

The coefficients 5 and -6 represent (5x - 6).

The last number 15 is the rem...