1. Bell Problem
Perform the indicated operation.
(x -5)(x2 – 5x + 7)

2. 5.4 Factor and Solve Polynomial Equations
Standards:
Understand patterns
Use models to understand relationships

3. Factoring Quadratic Equations
Type
Example
General Trinomial
2x2 – 3x - 20
Perfect square trinomial
x2 + 8x + 16
Difference of two squares
9x2 - 1
Common monomial factor
8x2 + 20x

4. Factor Ex. 5x2 – 17x + 6
Ex. x2 – x – 6
Ex. x2 – 4
Ex. 4x2 + 16x

5. Factoring Polynomials
A factorable polynomial with integer coefficients is factored completely if it is written as a product of unfactorable polynomials with integer coefficients
Not Factored Completely
3x(x2 – 4)
Factored Completely
2(x +1)(x – 4)
5x2(x2 – 3)

6. Ex. Factor the polynomial completely.
x3 + 2x2 – 15x
b. 2y5 – 18y3
c. 4z4 – 16z3 + 16z2

7. Homework
pg. 356 #3-9 all

8. Bell Problem
Factor the polynomial completely.
x3 – 7x2 + 10x

9. Perfect Cubes

10. Special Factoring Patterns
Sum of Two Cubes
a3 + b3 = (a + b)(a2 – ab + b2)
Difference of Two Cubes
a3 - b3 = (a - b)(a2 + ab + b2)

11. Factor
Ex. 8x Ex. 64x3 - 1

12. Factor by Grouping
Ex. Factor the polynomial x3 – 3x2 – 16x + 48 completely.

13. Ex. Factor completely.
16x4 – 81
2p8 + 10p5 + 12p2
x3 + 7x2 – 9x - 63

14. Ex. What are the real-number solutions of the equation
Ex. What are the real-number solutions of the equation 3x5 + 15x = 18x3?

15. Ex. Find the real-number solutions of the equation.
4x5 – 40x3 + 36x = 0
2x5 + 24x = 14x3

16. Homework
5.4 Practice B worksheet #2-28 even