1. Dividing Polynomials

2. Synthetic Division - To use synthetic division:
divide a polynomial by a polynomial
To use synthetic division:
There must be a coefficient for every possible power of the variable.
The divisor must have a leading coefficient of 1.

3. Step #1: Write the terms of the. polynomial so the degrees are in
Step #1: Write the terms of the polynomial so the degrees are in descending order.
Since the numerator does not contain all the powers of x, you must include a 0 for the

4. 5 -4 1 6 Since the divisor is x-3, r=3
Step #2: Write the constant r of the divisor x-r to the left and write down the coefficients. 5 -4 1 6
Since the divisor is x-3, r=3

5. Step #3: Bring down the first coefficient, 5.

6. 15 15 5 Step #4: Multiply the first coefficient by r, so
and place under the second coefficient then add. 5 15 15

7. Step #5: Repeat process multiplying. the sum, 15, by r;
Step #5: Repeat process multiplying the sum, 15, by r; and place this number under the next coefficient, then add. 5 15 45 41

8. Step #5 cont.: Repeat the same procedure.
Where did 123 and 372 come from? 5 15 45 41
123
372
124
378

9. Step #6: Write the quotient.
The numbers along the bottom are coefficients of the power of x in descending order, starting with the power that is one less than that of the dividend. 5 15 45 41
123
124
372
378

10. The quotient is:
Remember to place the remainder over the divisor.

11. Ex 7:
Step#1: Powers are all accounted for and in descending order.
Step#2: Identify r in the divisor.
Since the divisor is x+4, r=-4 .

12. 4 -4 20 8 -5 -1 1 -2 10 Step#3: Bring down the 1st coefficient.
Step#4: Multiply and add.
Step#5: Repeat. 4 -4 20 8 -5 -1 1 -2 10

13. Ex 8:
Notice the leading coefficient of the divisor is 2 not 1.
We must divide everything by 2 to change the coefficient to a 1.

14. 3

15. *Remember we cannot have complex fractions - we must simplify.

16. Ex 9: 1
Coefficients