1. 5.5 Apply the Remainder and Factor Theorem

2. Long Division
Polynomial Long Division: process used to divide polynomials.
Divide f(x) = 3x4 – 5x + 4x – 6 by x3 – 3x + 5

3. Divide f(x) = x3 + 5x – 7x + 2 by x – 2

4. Solve Using Long Division
(1) (2x4 + x3 + x – 1) ÷ (x2 + 2x – 1)
(2) (x3 – x2 + 4x – 10) ÷ (x + 2)

5. Synthetic Division
Synthetic Division can be used to divide any polynomial by a divisor of the form x – k.
(EX) Divide 2x3 + x2 – 8x + 5 by x + 3
Step 1: Set x + 3 = 0 and solve for x.
Step 2: Use Synthetic substitution to find the remainder.
Step 3: All numbers below the line will be used for the final answer.

6. Factor Theorem
If synthetic division is used and the remainder is determined to be 0, then the divisor (x – k) is a factor of the polynomial.
If (x – k) is a factor, then you can find the remaining factors of the polynomial by using synthetic substitution.

7. Factor the Polynomial
Factor f(x) = 3x3 – 4x – 28x – 16 completely given that x + 2 is a factor.
Step 1: Use synthetic substitution
Step 2: Factor the Quotient
Reminder: The remainder must be zero before factoring the quotient.

8. Practice Problems
Page 364 (3-6)

9. CW/HW
Page 366 (9,11,13,15,21,23)