1. Factoring by Grouping
Objective: After completing this section, students should be able to factor polynomials by grouping.
After working through this slideshow, you will be ready to factor by grouping.
Standard CA 11.0: Factor polynomials by grouping.

2. Steps for factoring by grouping:
1. A polynomial must have 4 terms to factor by grouping.
2. We factor the first two terms and the second two terms separately. Use the rules for GCF to factor these.

3. Examples: These two terms must be the same.

4. Examples:
These two terms must be the same.
You must always check to see if the expression is factored completely. This expression can still be factored using the rules for difference of two squares. (see 6.2)
This is a difference of two squares.

5. Examples: These two terms must be the same.
You can rearrange the terms so that they are the same.
These two terms must be the same.
But they are not the same. So this polynomial is not factorable.

6. Try These:
Factor by grouping.

7. Solutions:
If you did not get these answers, click the green button next to the solution to see it worked out.

8. BACK

9. When you factor a negative out of a positive, you will get a negative.
BACK

10. Now factor the difference of squares.
BACK

11. BACK

12. Factor by Grouping
Goal: To be able to factor polynomials with 4 terms by grouping

13. When…… When does it work? Always
When should I use it? For any polynomial but especially when you have 4 or more terms.

14. Steps Put ( ) around first 2 terms and last 2 terms
Factor out a common factor so what is left in the binomials is the same
Make the numbers you factored out into a binomial and multiply it by 1 of the same binomials

15. Use when there are 4 Terms 6x3 – 9x2 + 4x - 6
Factoring by Grouping
Use when there are 4 Terms
6x3 – 9x2 + 4x - 6 +
3x2(2x – 3)
2(2x – 3)
(2x – 3)
( 3x2 + 2)

16. Use when there are 4 Terms x3 + x2 + x + 1
Factoring by Grouping
Use when there are 4 Terms
x3 + x2 + x + 1 +
x2( x + 1)
1( x + 1)
(x + 1)
( x2 + 1)

17. Use when there are 4 Terms x3 + 2x2 - x - 2
Factoring by Grouping
Use when there are 4 Terms
x3 + 2x2 - x - 2 -
x2( x + 2)
1( x + 2)
(x + 2)
( x2 - 1)
(x + 2)
( x - 1)(x + 1)

18. Factor completely if possible… 8x3 + 2x2 + 12x +3

19. Factor completely if possible… 4x3 - 6x2 - 6x + 9

20. Factor completely if possible… 4x3 - 6x2 - 6x + 9