1. Remainder and Factor Theorems

2. The Remainder Theorem
If a polynomial f(x) is divided by x-a, the remainder is the constant f(a), and
Dividend=quotient *divisor +remainder
Where is a polynomial with degree one less than the degree of f(x)

3. Remember Lesson 5-3 for Synthetic Division
The Remainder Theorem
Remember Lesson 5-3 for Synthetic Division

4. The Remainder Theorem
Remainder = 1

5. Since the remainder is 0, x-3 is a factor of the polynomial.
The Factor Theorem
Since the remainder is 0, x-3 is a factor of the polynomial.

6. The Factor Theorem
When you divide the polynomial by one of the binomial factors , the quotient is called a depressed equation.

7. The Factor Theorem
Remainder = 10, therefore
(x-2)
Is NOT a factor

8. The Factor Theorem
Given a polynomial and one of its factors, find the remaining factors of the polynomial. Some factors may not be binomials.