1. Polynomial Division and Using Division to Solve More Difficult Polynomials

2. Dividing Polynomials
Two options:
Long Division
Synthetic Division

3. Long Division
Divide 134 by 5 using long division.

4. Polynomial Long Division
Find the quotient and the remainder of

5. Polynomial Long Division
Find the quotient and the remainder of

6. Let’s try the same example with Synthetic Division
Find the quotient and the remainder of
using synthetic division

7. Synthetic Division
Find the quotient and the remainder of

8. Remainder Theorem
If a polynomial is divided by x – a, then the remainder = f(a)
Example:
Find f(-2)

9. Factor Theorem
x – a is a factor of f(x) only if the remainder is zero (or f(a) = 0)
Example:
Show that x – 2 and x + 3 area factors of

10. Using Division to Solve Polynomials
Use synthetic division to show that x +4 is a factor of Then, factor the polynomial completely.

11. Using Division to Solve Polynomials
The polynomial has 3 zeros. If x = -3 is one of the zeros, find the remaining two roots.

12. Rational Roots (Zeros) Test
Every rational zero that is possible for a given polynomial can be expressed as the factors of the constant term divided by the factors of the leading coefficient.

13. Solving Using the Rational Root Test
List all possible rational roots for the polynomial y = 10x³ - 15x² - 16x Then, divide out the factor and solve for all remaining zeros.

14. Rational Roots Test
List all possible rational roots for the polynomial y = x³ - 7x – 6. Then, divide out the factor and solve for all remaining zeros.

15. Practice
Pg. 61 (1 – 13 odd, 19, 21)
Pg. 84 (21, 22)