1. Dividing Polynomials Long Division A little review:
Ex 1: Factor completely.
Ex 2: Divide

2. Division Algorithm
f (x) = d (x) q (x) +r (x) where f (x) is the dividend, d (x) is the divisor, q (x) is the quotient, and r (x) is the remainder.
Ex 3: Divide:
Ex 4: Divide:

3. Synthetic Division
Ex 5:
Ex 6:

4. The Remainder Theorem
If the polynomial f (x) is divided by x - k, then the remainder is the value of f (k).
Ex 7: Evaluate P (-4) for P(x) = x4 - 5x2 + 4x + 12.
Ex 8: Evaluate P (-1) for P(x) = 2x4 + 6x3 - 5x

5. The Factor Theorem
A polynomial f (x) has a factor x – k if and only if
f (k) = 0.
Ex 9: Show that (x – 2) and (x + 3) are factors of
f (x) = 2x4 + 7x3 - 4x2 – 27x – 18.
They are both factors of f (x) since f (2) and f (-3) both
equal 0.

6. Practice Assignment:
Section 2.3A (pg ) #1-44