1. Synthetic Division of Polynomials
Connections Unt G.8 - Synthetic Division of Polynomials
Monday, Feb 7, 2011
Synthetic Division of Polynomials
Be able to use synthetic division to divide polynomials.
Unit G.8

2. Synthetic Division
There is another way to divide polynomials called synthetic division.
This method can only be used when the divisor (the polynomial that you are dividing by) is in the form (x – a), where a is a number.
If the coefficient of x in the divisor is any number other than 1, you cannot use synthetic division.
FHS
Polynomials

3. Example Divide The divisor is , so a is 3.
Write a in the upper right corner and then write the coefficients of the dividend.
Draw a horizontal line and the bring down the first coefficient. 2 3 2 -1
-10
FHS
Polynomials

4. Example (cont.)
Multiply the 2 by the 3 and put the product in the second column.
Add the numbers in the column.
Multiply the sum by the 3 and put the product in the third column.
Add the numbers in the column. Draw a box around the last number. 6 15 2 5 5
FHS
Polynomials

5. Example (cont.)
The numbers on the bottom row are the coefficients of the quotient (the answer), and the last number is the remainder.
So the quotient of the example is: 6 15 2 5 5
FHS
Polynomials

6. We write the quotient this way:
Examples to Try .
Hint: a = – 2
We write the quotient this way:
– 2 4 7 10
– 8 2 4
– 1 12
FHS
Polynomials

7. We write the quotient this way:
Examples to Try
a = 5
We write the quotient this way: 5 2
– 6
– 12 10 20 2 4 8
FHS
Polynomials