1. 6-7 The Division Algorithm & The Remainder Theorem dividend=quotient. divisor + remainder If a polynomial f(x) is divided by x - c, the remainder is the constant r(x), and f(x) = q(x). (x - c) + r(x) where q(x) is a polynomial with degree one less than the degree of f(x). 21 = 4. 5 + 1 remainder r(x) = f(c)

2. ► If ► Find f(6) ► Method 1: Synthetic Substitution: use synthetic division ► Method 2: Direct Substitution 620-58-7 12724022460 212674102453 ► Synthetic Substitution: When synthetic division is used to evaluate a function.

3. Example Problem 1 Find the remainder of divided by x + 1 Use the Remainder Theorem!!!

4. Factors of Polynomials ► Depressed Polynomial: When you divide a polynomial by one of its binomial factors, the quotient is called a depressed polynomial. Depressed Polynomial

5. The Factor Theorem The binomial x - c is a factor of the polynomial f(x) if and only if f(c) = 0. Example Problem 2 Use the factor theorem to determine whether the function has the factor x + 3. Then find the remaining factors. See if f(-3) = 0, cause if it does then x + 3 is a factor

6. Using Synthetic Division, you can find the depressed polynomial and then factor from there. -316-1-30 -3-930 13-100 Factor: x + 3 Factored down to…

7. Homework Assignment #37 p. 359 11-29 odd, 34-37, 46-47