1. 5-4 Dividing Polynomials Synthetic Division
Today’s Objective:
I can divide polynomials

2. Why do I need to divide polynomials?
Find all zeros: 𝑓 𝑥 = 𝑥 5 −6 𝑥 𝑥 3 −60 𝑥 2 +99𝑥−54
Graphing:
Only finds real zeros.
Factoring:
Easiest way to factor is to divide out a known factor.
Dividing Terms
P(x): Dividend
D(x): Divisor
Q(x): Quotient
R(x): Remainder
Solution:

3. Long Division with Polynomials
multiply
Scratch work
Bring down next term
subtract

4. Long Division with Polynomials
You must have all terms listed
multiply
Scratch work Mental work
Bring down next term
subtract

5. Synthetic Division Coefficient of each term of dividend
Root or Zero of divisor
Add
multiply
Remainder

6. Synthetic Division Coefficient of each term of dividend
Root or Zero of divisor
Add
multiply
Remainder

7. Synthetic Division Coefficient of each term of dividend
Root or Zero of divisor
Add
multiply
Remainder

8. Synthetic Division Coefficient of each term of dividend
Root or Zero of divisor
Add
multiply
Because root was divided by 5
Divide quotient by 5, except the remainder

9. Synthetic Division Coefficient of each term Root or Zero of divisor
Add
multiply
Because root was divided by 7
Divide quotient by 7, except remainder