1. Remainder and Factor Theorem
Chapter 2.5

2. Synthetic Division
Synthetic division is a method used to divide any polynomial by a divisor in the form 𝑥−𝑘

3. Evaluate a function using synthetic substitution
1. Divide 𝑓 𝑥 = 2𝑥 3 + 𝑥 2 −8𝑥+5 by 𝑥 +3

4. Evaluate a function using synthetic substitution
2. Divide 𝑓 𝑥 = 𝑥 2 +3𝑥−6 by 𝑥+5

5. Evaluate a function using synthetic substitution
3. Divide 𝑓 𝑥 = 𝑥 2 +4 by 𝑥−2

6. Evaluate a function using synthetic substitution
4. Divide 𝑓 𝑥 = 2𝑥 3 + 9𝑥 2 +14𝑥+5 by 𝑥−3

7. Evaluate a function using synthetic substitution
5. Divide 𝑓 𝑥 = 𝑥 2 +2𝑥−11 by 𝑥+2

8. Factor a Polynomial completely given a factor.
1. 𝑓 𝑥 = 3𝑥 3 −4 𝑥 2 −𝑥−1;𝑥+2

9. Factor a Polynomial completely given a factor.
2. 𝑓 𝑥 = 2𝑥 3 −11 𝑥 2 +3𝑥+36;𝑥−3

10. Factor a Polynomial completely given a factor.
3. 𝑓 𝑥 = 𝑥 3 − 𝑥 2 −21𝑥+45;𝑥+5

11. Factor a Polynomial completely given a factor.
4. 𝑓 𝑥 = 4𝑥 3 − 4𝑥 2 −9𝑥+9;𝑥−1

12. Given a zero of the function, find the other zeroes
1. 𝑓 𝑥 = 𝑥 3 −2 𝑥 2 −23𝑥+60;𝑥=3

13. Given a zero of the function, find the other zeroes
2. 𝑓 𝑥 = 𝑥 3 + 𝑥 2 −16𝑥−16;𝑥=4

14. Given a zero of the function, find the other zeroes
3. 𝑓 𝑥 = 𝑥 3 +2 𝑥 2 −20𝑥+24;𝑥=−6

15. Given a zero of the function, find the other zeroes
4. 𝑓 𝑥 = 2𝑥 3 +3 𝑥 2 −39𝑥−20;𝑥=4