1. Multiply together

2. Factoring Polynomials
Section 5-4
Pages

3. Objectives I can factor a polynomial using the following methods: GCF
Reverse FOIL
Difference of Two Squares
Swing & Divide
Grouping
Sum of Two Cubes
Difference of Two Cubes

4. Review: What is Factoring?
Factoring is a method to find the basic numbers that made up a newly formed product.

5. Review In Chapter 4 we already covered these methods:
GCF
Difference of Two Squares
Reverse FOIL
Swing & Divide
Now we will be looking at the other three methods

6. Sum of Two Cubes a3 + b3 = (a + b)(a2 – ab + b2) a3 + b3 =
Here is the factoring rule:
a3 + b3 = (a + b)(a2 – ab + b2)

7. Example 1 8x3 + 27 (2x)3 + (3)3 So a = 2x and b = 3
Factors are (a + b)(a2 – ab + b2)
So: (2x + 3)(4x2 – 6x + 9)

8. Example 2 x3 + 64 (x)3 + (4)3 So a = x and b = 4
Factors are (a + b)(a2 – ab + b2)
So: (x + 4)(x2 – 4x + 16)

9. Difference of Two Cubes
a3 - b3 =
Here is the factoring rule:
a3 - b3 = (a - b)(a2 + ab + b2)

10. Example 1 64x3 - 1 (4x)3 - (1)3 So a = 4x and b = 1
Factors are (a - b)(a2 + ab + b2)
So: (4x - 1)(16x2 + 4x + 1)

11. Example 2 8x3 - 125 (2x)3 - (5)3 So a = 2x and b = 5
Factors are (a - b)(a2 + ab + b2)
So: (2x - 5)(4x2 + 10x + 25)

12. Grouping Method 4 Terms
The grouping method uses a combination of GCF factoring with distributive property
ra + rb + sa + sb
(ra + rb) + (sa + sb)
r(a + b) + s(a + b)
(r + s)(a + b)

13. Example 1 x3 – 3x2 – 16x + 48 (x3 – 3x2) +(-16x + 48)

14. Example 2 x3 – x2 + 2x - 2 (x3 – x2) +(2x - 2) x2(x – 1) + 2(x – 1)

15. Homework
Worksheet 10-4
TAKs Packet Objective #5 due next Monday