1. Warm-Up Which of the following does not belong? 2 17 5 23 10 59 37 3
Primes 2 17 5 23 10 59 37 3

2. Factoring!
Objectives:
To factor “special pattern” binomials

3. Factoring: Polynomials
When factoring a polynomial, you have to write it as the product of prime polynomials.
Prime factors

4. Flowchart
A flowchart is a type of diagram that helps steer you through a complex process.

5. Flowchart
The factoring flowchart is a simple device that will guide us through the complex process of factoring a polynomial. According to the chart, what is the first step in factoring a polynomial?

6. Greatest Common Factor
The fist step in factoring a polynomial is to use the distributive property backwards to take out the greatest common factor.
Quotient
GCF
Taking out the GCF first will make factoring the rest of the polynomial much easier.

7. Factoring: Polynomials
If your polynomial has no GCF or you’ve already factored it out, what is the next step in factoring your polynomial?

8. Factoring: Polynomials
The next step depends on how many terms your polynomial has: 2, 3, or 4 or more.

9. Factoring: Binomials
The binomial case is easy; it’s based on patterns. The first is the difference of two squares: So going backwards…
Square root of 2nd term
Difference of
2 Squares
Square root of 1st term

10. Difference of Two Squares

11. Sum of Two Squares
A sum of two squares is prime! No work! Ex) Factor Prime!

12. Examples:
Factor.
16x2 – 1
16x4 – 1
−9x2 + 4y2

13. Examples

14. Sneedlegrit:
Factor.
9x2 – 4

15. Factoring: Polynomials
If your binomial is not the difference of two squares, maybe it is the sum or difference of two cubes.

16. Sum or Difference of Two Cubes
Sum of Two Cubes Difference of Two Cubes

17. Examples:
Factor.
x3 – 27
6x3 + 6y3

18. Examples
Factor.
3. x
4. 8x3 – 27y3
5. x6 – y6

19. Sneedlegrit:
Factor.
2. x3 – 8

20. HW: pg.38 (19 – 28, 39 – 46) All