1. Factoring Polynomials by Grouping
Section 5.4(d)
Factoring Polynomials by Grouping

2. Group the terms
with common
variables and factor
V. Factor by Grouping (4-terms)
( ) ( )
a2x - b2x + a2y -b2y
Both terms have an x
Both terms have a y
x(a2 - b2) + y(a2 - b2)
Both terms have (a2 - b2)
(a2 - b2)( ) x + y
Can you go farther?

3. (cont.)
Difference of 2 squares
(a2 - b2)( x + y )
(a + b)(a - b)(x + y)

4. * * * * Factor by grouping: 4x2 + 7x + 3 a.) 4•3 = 12 12 x 1 6 x 2
Factors of 12 * *
a.) 4•3 = 12
12 x 1
6 x 2
4 x 3
= 13
b.)
Add the factors
6 + 2 = 8
Why?
4 + 3 = 7
Look for factors
that add to 7
Why?

5. ( ) ( ) (cont.) Now rearrange the original trinomial 4x2 + 7x + 3
Separate the middle
term (7x) into 2 pieces:
4x and 3x
4x2 + 7x + 3
4x2 + 4x + 3x + 3
Why?
4 + 3 = 7
c.) Now group the first 2 terms
and the last 2 terms
4x + 3x = 7x
( ) ( )
4x2 + 4x + 3x + 3

6. ( ) ( ) ( ) ( 4x + 3 ) (cont.) 4x2 + 4x + 3x + 3
( ) ( )
4x2 + 4x + 3x + 3
d.) Look for a GCF (greatest common factor)
in each term
4x(x + 1) + 3(x + 1)
e.) Look for a GCF in each term again
( )
4x(x + 1) + 3(x + 1)
(x + 1)
( 4x )
(x + 1)(4x + 3)
Done

7. (cont.) Check by “foiling” (distributing)
(x + 1)(4x + 3) =
4x2
+ 3x
+ 4x
+ 3
= 4x2 + 7x + 3

8. 29.)
Factor by grouping

9. 30.)
Factor by grouping

10. 31.)
Factor by grouping

11. V. Factor trinomial by any method
32.)
Factor

12. 33.)
Factor

13. 34.)
Factor

14. Homework
Page
Problems # 16, and