 # Objective: 6.4 Factoring and Solving Polynomial Equations 1 5 Minute Check  Simplify the expression. 1. 2. 3. 4.

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Objective: 6.4 Factoring and Solving Polynomial Equations 1 5 Minute Check  Simplify the expression. 1. 2. 3. 4.

2 What you will learn today…  How to factor a trinomial expression  How to use factoring to solve a polynomial equation

Objective: 6.4 Factoring and Solving Polynomial Equations 3 Factoring We Have Learned General trinomial: 2x 2 –5x–12 = (2x + 3)(x - 4) Perfect square trinomial: x 2 + 10x + 25 = (x + 5) 2 Difference of two squares: 4x 2 – 9 = (2x + 3)(2x – 3) Common Monomial: 6x 2 + 15x = 3x(2x + 5)

Objective: 6.4 Factoring and Solving Polynomial Equations 4 New Factoring Patterns Sum of Two Cubes: a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) Example: x 3 + 8 = (x+2)(x 2 – 2x + 4) Difference of Two Cubes: a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) Example: 8x 3 – 1 = (2x-1)(4x 2 + 2x + 1)

Objective: 6.4 Factoring and Solving Polynomial Equations 5 Examples  Factor each polynomial. A. x 3 + 27B. 16u 5 – 250u 2

Objective: 6.4 Factoring and Solving Polynomial Equations 6 You Try  Factor each polynomial A. 125 + x 3 #35 on homework

Objective: 6.4 Factoring and Solving Polynomial Equations 7 Factoring by Grouping  Factor: x 3 – 2x 2 – 9x + 18

Objective: 6.4 Factoring and Solving Polynomial Equations 8 You Try  #43 on homework

Objective: 6.4 Factoring and Solving Polynomial Equations 9 Factoring Polynomials in Quadratic Form  Factor: A. 81x 4 – 16B. 4x 6 - 20x 4 + 24x 2

Objective: 6.4 Factoring and Solving Polynomial Equations 10 You Try  Factor: A. 25x 4 – 36

Objective: 6.4 Factoring and Solving Polynomial Equations 11 Solving Polynomial Equations  Solve 2x 5 + 24x = 14x 3

Objective: 6.4 Factoring and Solving Polynomial Equations 12 You Try  #70 on homework

Objective: 6.4 Factoring and Solving Polynomial Equations 13 Homework  page 348, 18-22 even, 33-37 odd, 41-45 odd, 51-53 odd, 59-63 odd, 69, 70, 71, 73, 76, 77, 78, 87

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