Essential Question: Describe two methods for solving polynomial equations that have a degree greater than two.

6-4: Solving Polynomial Equations Remember that a difference of perfect squares has a special factoring pattern. x 2 – 4 = (x + 2)(x – 2) A cubic sum of cubes and difference of cubes also have special factoring patterns. a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) Example: Factor x 3 – 8 Cube root of x 3 ? x Cube root of 8? 2 (x – 2)(x 2 + 2x ) = (x – 2)(x 2 + 2x + 4)

6-4: Solving Polynomial Equations Your Turn Factor 8x 3 – 1 Factor 27x Solving? On the board (2x – 1)(4x 2 + 2x + 1) (3x + 4)(9x 2 – 12x + 16)

6-4: Solving Polynomial Equations Assignment Page 330 Problems 12 – 20 (all problems) You must show work for credit Remember “=0” means you set each “(…)” equal to 0 and solve No “=0” means you simply factor

Essential Question: Describe two methods for solving polynomial equations that have a degree greater than two.

6-4: Solving Polynomial Equations You can sometimes solve polynomials of a higher degree if they follow a pattern of a lower degree. Factor x 4 – 2x 2 – 8 Let x 2 = a Then x 4 = x 2 · x 2  a · a = a 2 This gives us: a 2 – 2a – 8, which can be factored (a – 4)(a + 2) Substitute x 2 back in for a, factor anything left you can (x 2 – 4)(x 2 + 2) (x – 2)(x + 2)(x 2 + 2)

6-4: Solving Polynomial Equations Your Turn Factor x 4 + 7x Factor x 4 – 3x 2 – 10 Solving? On the board (x 2 + 1)(x 2 + 6) (x 2 – 5)(x 2 + 2)

6-4: Solving Polynomial Equations Assignment Page 330 Problems 21 – 32 (all problems) You must show work for credit Remember “=0” means you set each “(…)” equal to 0 and solve No “=0” means you simply factor