1. Warm - up 6.4 1. 4x2 – 24x 4x(x – 6) 2. 2x2 + 11x – 21 (2x – 3)(x + 7)
Factor:
1. 4x2 – 24x
4x(x – 6)
2. 2x2 + 11x – 21
(2x – 3)(x + 7)
3. 4x2 – 36x + 81
(2x – 9)2
Solve:
4. x2 + 10x + 25 = 0
x = -5
5. 6x2 + x = 15
x = 3/2 and -5/3

2. 6.4 solving polynomial equations
Objective – To be able to factor and solve polynomial expressions.
CA State Standard
- 3.0 Students are adept at operations on polynomials, including long division.
- 4.0 Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes.
by Jason L. Bradbury

3. 6.4 solving polynomial equations
In Ch. 5 we learned how to factor:
- A General Trinomial
2x2 – 5x – 12
(2x + 3)(x – 4)
- A Perfect Square Trinomial
x2 + 10x + 25
(x + 5)(x + 5) = (x +5)2
- The Difference of two Squares
4x2 – 9
(2x)2 – 32
(2x + 3)(2x – 3)
- A Common Monomial Factor
6x2 + 15x
3x(2x + 5)

4. (x2 + ?)(x2 – ?) (x2 + 3)(x2 – 9) (x2 + 3)(x – 3)(x + 3)
Example 1
Factor
a) x4 – 6x2 – 27
(x ?)(x2 – ?)
(x2 + 3)(x2 – 9)
(x2 + 3)(x – 3)(x + 3)
b) x4 – 3x2 – 10
(x ?)(x2 – ?)
(x2 + 2)(x2 – 5)

5. a = x x3 + 23 ex. x3 + 8 b = 2 (x + 2)(x2 – 2x + 4) a = 2x b = 1
** Special Factoring Patterns
Sum of Two Cubes
a3 + b3 = (a + b)(a2 - ab + b2)
a = x
x3 + 23
ex. x3 + 8
b = 2
(x + 2)(x2 – 2x + 4)
Difference of Two Cubes
a = 2x
a3 – b3 = (a – b)(a2 + ab + b2)
b = 1
ex x3 – 1
(2x – 1)(4x2 + 2x + 1)
(2x)3 – (1)3
Example 2 x
a3 + b3 = (a + b)(a2 - ab + b2)
x3 + 53
= (x + 5)(x2 – 5x + 25)

6. Example 3 a) x3 – 27 x3 – 33 = (x – 3)(x2 + 3x + 9) b) 8x3 + 64
Factor
a) x3 – 27
a3 – b3 = (a – b)(a2 + ab + b2)
x3 – 33
= (x – 3)(x2 + 3x + 9)
b) 8x3 + 64
a3 + b3 = (a + b)(a2 - ab + b2)
(2x)3 + (4)3
= (2x + 4)(4x2 – 8x + 16)

7. Extra Example 2 x3 – 2x2 – 9x + 18 x2(x – 2) -9(x – 2)
Factor by grouping
x3 – 2x2 – 9x + 18
x2(x – 2)
-9(x – 2)
Must be the same
(x2 – 9)(x – 2)
(x – 3)(x + 3)(x – 2)

8. 6.4 Homework
Page 336 – 337
12 – 14, 21 – 27, and 31

9. 6.4 Guided Practice
Page 336 – 337
12 – 14 and 21 – 24