1. Synthetic Division Notes
12/18/2014
Dividing Polynomials

2. Simple Division -
dividing a polynomial by a monomial

3. Simplify

4. Simplify

5. 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 be a binomial of degree one

6. 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 dividend does not contain all the powers of x, you must include a 0 for the

7. Since the divisor is x-3, r=3
Step #2: If divisor is (x – r), then set x – r = 0 and solve for x, therefore x = r 5 -4 1 6
Since the divisor is x-3, r=3

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

9. 5 15 15 Step #4: Multiply the first coefficient by r, so
and place under the second coefficient then combine. 5 15 15

10. 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 combine. 5 15 45 41

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

12. 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

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

14. 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 .

15. Synthetic Division Notes
12/18/2014
Step#3: Bring down the 1st coefficient.
Step#4: Multiply and add.
Step#5: Repeat. 4 -4 20 8 -5 -1 1 -2 10

16. Ex 8:
Notice the leading coefficient of the divisor is 3 not 1.
We still solve divisor for x; 3x + 1 = 0
x =

17. -2 -1 1 -3 2 6 3
Because the binomial’s leading coefficient = 3; I divide ALL coefficients by 3 – NOT THE REMAINDER!!

18. (4g2 – 9) * (2g + 3)-1 -6 9 4 -6
Divide answers by 2:
2x – 3