1. Opener Perform the indicated operation.
6−4 𝑥 2 +5 𝑥 3 − 7 𝑥 2 − 𝑥 4 −12 𝑥 3
(𝑥−6)(2𝑥+1)(5𝑥−3)
Use synthetic substitution to evaluate
𝑓 𝑥 = 𝑥 3 −2𝑥−1 when 𝑥=3
Solve 6 𝑥 2 +𝑥=15

2. Factoring and Solving Polynomial Equations
Notes: 6.4
Factoring and Solving Polynomial Equations

3. Factoring Patterns Sum of Two Cubes 𝑎 3 + 𝑏 3 =(𝑎+𝑏)( 𝑎 2 −𝑎𝑏+ 𝑏 2 )
Difference of Two Cubes
𝑎 3 − 𝑏 3 =(𝑎−𝑏)( 𝑎 2 +𝑎𝑏+ 𝑏 2 )

4. Problem Set 1: Factoring the Sum or Difference of Two Cubes
𝑥 3 +27
16 𝑢 5 −250 𝑢 2
125+ 𝑥 3
64 𝑎 4 −27𝑎

5. Problem Set 2: Factor by Grouping
𝑥 3 −2 𝑥 2 −9𝑥+18
𝑏 𝑥 2 +3𝑎+3𝑏+𝑎 𝑥 2
𝑥 2 𝑦 2 −3 𝑥 2 −4 𝑦 2 +12

6. Problem Set 3: Factoring Polynomials in Quadratic Form
81 𝑥 4 −16
4 𝑥 6 −20 𝑥 𝑥 2
25 𝑥 4 −36
𝑎 2 𝑏 2 −8𝑎 𝑏 𝑏 4

7. Problem Set 4: Solving a Polynomial Equation
2 𝑥 5 +24𝑥=14 𝑥 3
2 𝑦 5 −18𝑦=0