1. 21 = 4 . 5 + 1 P(x) = Q(x) . (x - r) + P(r) 4.3 The Remainder Theorem
dividend=quotient . divisor + remainder
If a polynomial P(x) is divided by x - r,
the remainder is the constant P(r), and
P(x) = Q(x) . (x - r) + P(r)
where Q(x) is a polynomial with degree one less than the degree of P(x).

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

3. Synthetic Division

4. The Factor Theorem
The binomial x - r is a factor of the polynomial P(x)
if and only if P(r) = 0.
Example Problem 2
Use the factor theorem to determine whether the function
has the factor x – 1.
See if f(1) = 0, cause if it does then x – 1 is a factor

5. Depressed Polynomial
When a polynomial is divided by one of its binomial factors x – r, the quotient is called a depressed polynomial.
x – 1 is a factor of 2x3 – 3x2 + x. Using synthetic division you can find the depressed polynomial to be 2x2 – x.

6. Review Example 4 & 5 on pg. 225
Take note of the graphing calculator tip
The remainder theorem can be used to determine missing coefficients