1. Factoring – General Method
You have learned a variety of methods for factoring. This section puts all of the methods together for a general factoring strategy.
It is very important that you can factor a polynomial without being told what method to use. In fact, sometimes several methods will be used on the same problem.

2. A simple version of the factoring strategy is given below.
Always factor the Greatest Common Factor first.
Determine how many terms are left in the resulting polynomial.
Factor using the methods for that number of terms.
After completing a step, always ask, can I factor again?
This is best described in the following diagram.

3. Greatest Common Factor
The Greatest Common Factor is always the first step in factoring.
If you leave this step out, the factoring can get extremely difficult or impossible. Don’t forget the GCF!

4. Greatest Common Factor
Two
Three
Four
How many terms are there?
The number of terms determines the possible methods to consider.

5. Greatest Common Factor
Two
Three
Four
Difference of Two Squares
Lets start with two terms.
Sum of Two Cubes
The possible factoring methods include …
Difference of Two Cubes

6. Greatest Common Factor
Two
Three
Four
Difference of Two Squares
Perfect Square Trinomial
If there are three terms.
Sum of Two Cubes
Trinomial:
Guess/Check or
ac Method
Difference of Two Cubes

7. Greatest Common Factor
Two
Three
Four
Difference of Two Squares
Perfect Square Trinomial
Grouping
Sum of Two Cubes
Trinomial:
Guess/Check or
ac Method
If there are four terms.
Difference of Two Cubes

8. Example 1
Factor:
Factor the GCF
Two terms are left in the resulting polynomial

9. Greatest Common Factor
Two
Three
Four
Difference of Two Squares
Perfect Square Trinomial
Grouping
Sum of Two Cubes
Trinomial:
Guess/Check or
ac Method
Difference of Two Cubes

10. Greatest Common Factor
Two
Difference of Two Squares
Sum of Two Cubes
Consider these three methods
Difference of Two Cubes

11. Example 1
Factor:
Factor the GCF
Two terms are left in the resulting polynomial
It’s a difference of two squares.
Any more factoring possible? No

12. Example 2
Factor:
Factor the GCF
Three terms are left in the resulting polynomial

13. Greatest Common Factor
Two
Three
Four
Difference of Two Squares
Perfect Square Trinomial
Grouping
Sum of Two Cubes
Trinomial:
Guess/Check or
ac Method
Difference of Two Cubes

14. Greatest Common Factor
Three
Perfect Square Trinomial
Check for a Perfect Square Trinomial first
Trinomial:
Guess/Check or
ac Method

15. Example 2
Factor:
Factor the GCF
Three terms are left in the resulting polynomial
It is a perfect square trinomial.

16. Any more factoring possible?No

17. Example 3
Factor:
Factor the GCF
None, other than 1
Four terms suggests the grouping method.

18. Any more factoring possible?
Yes, a difference of two squares.
Any more factoring possible? No

19. With factoring it is important to remember,
after completing a factoring step, always ask
Is there any more factoring possible?

20. END OF PRESENTATION