1. 6.4: Solving Polynomial Equations

2. Solving by Graphing 1. 3x 3 – 6x 2 – 9x =0 2. 6x 2 = 48x

3. 3. 2x 3 + 5x 2 = 7x 4. 12x 3 = 60x 2 + 75x

4. The volume V of a container is modeled by the function V(x) = x 3 – 3x 2 – 4x. Let x, x + 1, and x – 4 represent the width, the length, and the height respectively. The container has a volume of 70ft 3. Find the container’s dimensions.

5. Sum of Cubes (a 3 + b 3 ) = (a + b)(a 2 – ab + b 2 ) Difference of Cubes (a 3 – b 3 ) = (a – b)(a 2 + ab + b 2 )

6. Factor each expression. 1. x 3 + 125 2. 8x 3 – 1

7. Solve each equation. 1. 64x 3 + 8 = 0 2. x 3 – 27 = 0

8. Factor each expression. 1. x 4 – 8x 2 + 7 2. 4x 4 – 6x 2 + 2 3. x 4 – 7x 2 + 12

9. Solve each equation. 1. x 4 – 10x 2 + 9 = 0 2. x 4 – 12x 2 – 64 = 0 3. x 4 + 7x 2 – 18 = 0

10. Solve each equation. 1. x 3 + 2x 2 + x +2 = 0 2. 4x 3 + 3x 2 + 28x + 21 = 0 3. 2x 3 – 6x 2 + x – 3 = 0

11. S olve each equation. 1. 81x 3 – 192 = 0 2. -2x 4 + 46x 2 = -100 3. x 5 – 5x 3 + 4x = 0 4. 2x 4 – 14x 3 + 12x 2 = 0