1. Factoring Trinomials of the form
Chapter 5.4
Factoring Trinomials of the form
ax2 + bx + c

2. Grouping Method 1. Check to see if there is a GCF.
2. Find the grouping number a • c.
3. Find 2 integers whose product is the grouping number and sum is b.
4. Split bx as the sum of two terms.
5. Factor by grouping.

3. 4. Factor. 2 x2 + 7 x + 5 2x2 + 2x + 5x + 5 1. GCF = 1
2. Grouping Number.
2x2 + 2x + 5x + 5
(2)(5)
= 10
3. Find 2 integers whose
product is 10 and sum is 7.
1, 10
2, 5
4. Split into 2 terms. 1 2 3 4 5 6 7 8 9 10 11

4. 4. Factor. 2 x2 + 7 x + 5 2x2 + 2x + 5x + 5 2x 5 2x ( x + 1 ) + 5 ( x
5. Factor by grouping.
GCF = 2x
2x2
+ 2x
+ 5x
+ 5
GCF = 5 2x 5
GCF =
(x + 1) 2x ( x
+ 1 )
+ 5 ( x
+ 1 )
(x + 1)
(x + 1)
(x + 1)( ) 2x
+ 5 1 2 3 4 5 6 7 8 9 10 11

5. 5. Factor. 9 x2 – 64 x + 7 9x2 – x – 63x + 7 1. GCF = 1
2. Grouping Number.
9x2 – x – 63x + 7
(9)(7)
= 63
3. Find 2 integers whose
product is 63 and sum is -64.
-1, -63
4. Split into 2 terms. 1 2 3 4 5 6 7 8 9 10 11

6. 5. Factor. 9 x2 – 64 x + 7 9x2 – x – 63x + 7 x -7 x ( 9x – 1 ) – 7 (
5. Factor by grouping.
GCF = x
9x2
– x
– 63x
+ 7
GCF = -7 x -7
GCF =
(9x – 1) x ( 9x
– 1 )
– 7 ( 9x
– 1 )
(9x – 1)
(9x – 1)
(9x – 1)( ) x
– 7 1 2 3 4 5 6 7 8 9 10 11

7. 6. Factor. 3 x2 + 4 x – 4 3x2 – 2x + 6x – 4 1. GCF = 1
2. Grouping Number.
3x2 – 2x + 6x – 4
(3)(-4)
= -12
3. Find 2 integers whose
product is -12 and sum is 4.
-1, 12
-2, 6
4. Split into 2 terms. 1 2 3 4 5 6 7 8 9 10 11

8. 6. Factor. 3 x2 + 4 x – 4 3x2 – 2x + 6x – 4 x 2 x ( 3x – 2 ) + 2 ( 3x
5. Factor by grouping.
GCF = x
3x2
– 2x
+ 6x
– 4
GCF = 2 x 2
GCF =
(3x – 2) x ( 3x
– 2 )
+ 2 ( 3x
– 2 )
(3x – 2)
(3x – 2)
(3x – 2)( ) x
+ 2 1 2 3 4 5 6 7 8 9 10 11

9. 7. Factor. 8 x2 + 8 x – 6 2( ) 4 x2 + 4 x – 3 2(4x2 – 2x + 6x – 3 )
1. GCF = 2
2. Grouping Number.
2( ) 4 x2
+ 4 x
– 3
(4)(-3)
= -12
2(4x2 – 2x + 6x – 3 )
3. Find 2 integers whose
product is -12 and sum is 4.
-1, 12
-2, 6
4. Split into 2 terms. 1 2 3 4 5 6 7 8 9 10 11

10. 7. Factor. ( ) 8 x2 + 8 x – 6 2( ) 4 x2 + 4 x – 3 2( ) 4x2 – 2x + 6x
5. Factor by grouping.
2( ) 4 x2
+ 4 x
– 3
GCF = 2x
GCF = 3
GCF =
(2x – 1)
2( )
4x2
– 2x
+ 6x
– 3 2x 3 2 ( 2x
( ) 2x
– 1
+ 3
( ) 2x
– 1 )
(2x – 1)
(2x – 1) 2
(2x – 1)( ) 2x
+ 3 1 2 3 4 5 6 7 8 9 10 11

11. 8. Factor. 24 x2
– 38 x
+ 10
1. GCF = 2
2. Grouping Number.
2( ) 12 x2
– 19 x
+ 5
(12)(5)
= 60
2(12x2 – 4x – 15x + 5 )
3. Find 2 integers whose
product is 60 and sum is -19.
-1, -60
-2, -30
-3, -20
-4, -15
4. Split into 2 terms. 1 2 3 4 5 6 7 8 9 10 11

12. 8. Factor. ( ) 24 x2 – 38 x + 10 2( ) 12 x2 – 19 x + 5 2( ) 12x2 – 4x
5. Factor by grouping.
2( ) 12 x2
– 19 x
+ 5
GCF = 4x
GCF = -5
GCF =
(3x – 1)
2( )
12x2
– 4x
– 15x
+ 5 4x -5 2 ( 4x
( ) 3x
– 1
– 5
( ) 3x
– 1 )
(3x – 1)
(3x – 1) 2
(3x – 1)( ) 4x
– 5 1 2 3 4 5 6 7 8 9 10 11

13. Factoring Trinomials of the form
Chapter 5.4
Factoring Trinomials of the form
ax2 + bx + c