1. Lesson 6.4 Factoring and Solving Polynomial Equations

2. Vocabulary Factor by Grouping: a method used to factor some polynomials with pairs of terms that have a common monomial factor: ra + rb + sa + sb = r(a + b) + s (a + b) = (r + s)(a + b). Factor by Grouping: a method used to factor some polynomials with pairs of terms that have a common monomial factor: ra + rb + sa + sb = r(a + b) + s (a + b) = (r + s)(a + b). Quadratic Form: the form au 2 + bu + c where u is any expression in x. Quadratic Form: the form au 2 + bu + c where u is any expression in x.

3. Special Factoring Patterns Sum of Two Cubes Sum of Two Cubes –a 3 + b 3 = (a + b)(a 2 - ab +b 2 ) –Ex: x 3 + 8 = (x + 2)(x 2 -2x + 4) Difference of Two Cubes Difference of Two Cubes –a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) –Ex: 8x 3 – 1 = (2x – 1)(4x 2 + 2x + 1)

4. Example 1: Factoring the Sum or Difference of Cubes A) x 3 – 64 B) 125 + x 3 C) 54y 4 + 16y D) 64a 4 – 27a

5. Example 2: Factor by Grouping A) x 3 – 3x 2 – 4x + 12 B) x 3 – x 2 – 2x + 2 C) x 2 y 2 – 3x 2 – 4y 2 + 12

6. Example 3: Factoring Polynomials in Quadratic Form A) 16x 4 – 1 B) 2x 6 – 10x 4 + 12x 2 C) x 4 – 7x 2 + 12

7. Example 4: Solving a Polynomial Equation A) x 4 + 4 = 5x 2 B) x 5 – 2x = -x 3