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

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

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 )

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

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

Problem Set 3: Factoring Polynomials in Quadratic Form 81 𝑥 4 −16 4 𝑥 6 −20 𝑥 4 +24 𝑥 2 25 𝑥 4 −36 𝑎 2 𝑏 2 −8𝑎 𝑏 3 +16 𝑏 4

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