1. 2.2 D IVIDING POLYNOMIALS ; R EMAINDER AND F ACTOR T HEOREMS

2. R EVIEW O F F ACTORS What is a factor? How do you know if 4 is a factor of 50? Is 4 a factor of 124?

3. LONG DIVISION REVIEW 1 8 897 1 16 1 2 7 r1

4. L ONG D IVISION OF P OLYNOMIALS

5. E XAMPLE Divide using long division. State the quotient, q( x ), and the remainder, r( x ). (6x ³ +17x²+ 27x + 20) (3x + 4)

6. E XAMPLE Divide using long division. State the quotient, q( x ), and the remainder, r( x ).

7. R EMAINDERS CAN BE USEFUL ! THE REMAINDER THEOREM : If the polynomial P(x) is divided by (x – a), then the remainder is P(a).

8. S YNTHETIC D IVISION Quick method of dividing polynomials Used when the divisor is of the form x – a Last column is always the remainder

9. E XAMPLE Divide using synthetic division.

10. E XAMPLE Divide using synthetic division.

11. F ACTOR T HEOREM For a polynomial P(x), x-a is a factor if an only if P(a)=0 Or in other words, If f(c) = 0, then x – c is a factor of f(x). If x – c is a factor of f(x), then f(c) = 0. If we know a factor, we know a zero! If we know a zero, we know a factor!

12. PG. 61 # 20 You are given the polynomial and one of the roots are x= -2. Find the other roots.

13. PG. 61 # 22 You are given the polynomial two of the roots are x= -2 and x=3. Find the other roots.