Transcript 11.3 - Factoring General Trinomials Factoring Trinomials REVIEW:  x  bx  c 4 x  24 x  36 4  x 

11.3 - Factoring General Trinomials
Factoring Trinomials
REVIEW:
 x  bx  c
2
4 x  24 x  36
2
4  x  6x  9
2
Factors of 9 are: 1, 9
4 x
3, 3
 x
4  x  3 x  3

11.3 - Factoring General Trinomials
Factoring Trinomials
REVIEW:
 x  bx  c
2
5 x  25 x  30 x
5
4
3
5x  x  5x  6
3
Factors of 6 are: 1, 6
5x  x
2
2, 3
 x

3
5x  x  1 x  6
3
11.3 - Factoring General Trinomials
Factoring Trinomials
 ax  bx  c
2
4 x  12 x  5
2
Factors of 5 are: 1, 5
Factors of 4 are: 1, 4

x
2, 2

x
 2x  1 2x  5

11.3 - Factoring General Trinomials
Factoring Trinomials
 ax  bx  c
2
2 x  11x  12
2
Factors of 12 are:
1, 12
Factors of 2 are:
1, 2

x

2, 6
x
 x  4 2 x  3
3, 4

11.3 - Factoring General Trinomials
Factoring Trinomials
 ax  bx  c
2
35 x  4 x  4
2
Factors of 4 are: 1, 4
Factors of 35 are:

2,2
1, 35
x
5, 7

x
5x  2 7 x  2

11.3 - Factoring General Trinomials
Factoring Trinomials
12a  16ab  3b
2
 ax  bx  c
2
2
Factors of 3 are: 1, 3
Factors of 12 are:

a
1, 12
2, 6
b  a
3, 4
b 
 2a  3b 6a  b 
11.4 - Factoring Trinomials by Grouping
Factoring Trinomials
 ax  bx  c
2
4 x  12 x  5
2
Product of 4 and 5: 20
Factors of 20 are: 1, 20 2, 10 4, 5
Factors of 20 that combine to 12:
4x2 + 2x + 10x + 5
2x  2 x  1  5  2 x  1
 2 x  1  2 x  5
2, 10
11.4 - Factoring Trinomials by Grouping
Factoring Trinomials
 ax  bx  c
2
2 x  11x  12
2
Product of 2 and 12:
24
Factors of 24 are: 1, 24 2, 12 3, 8 4, 6
Factors of 24 that combine to 11:
2x2 - 3x -
8x + 12
x  2 x  3  4  2 x  3
 2 x  3  x  4 
3, 8
11.4 - Factoring Trinomials by Grouping
Factoring Trinomials
 ax  bx  c
2
35 x  4 x  4
2
Product of 35 and 4:
140
Factors of 140 are: 1, 140 2, 70 4, 35 5, 28
7, 20 10, 14
Factors of 140 that combine to 4: 10, 14
35x2 - 10x + 14x -
4
5x 7 x  2   2 7 x  2 
7 x  2   5 x  2 
11.4 - Factoring Trinomials by Grouping
Factoring Trinomials
12a  16ab  3b
2
 ax  bx  c
2
2
Product of 12 and 3:
36
Factors of 36 are: 1, 36 2, 18 3, 12 4, 9 6, 6
Factors of 36 that combine to 16:
12a2 + 2ab - 18ab - 3b2
2a 6a  b   3b 6a  b 
6a  b 2a  3b
2, 18
11.5 – Factoring Perfect Square Trinomials
and the Difference of Two Squares
Perfect Square Trinomials
x  12 x  36 
x  13 x  36 
2
2

 x

 x  6 x  6
2
x  6
x

x
 x

x  4x  9
Not a perfect square
11.5 – Factoring Perfect Square Trinomials
and the Difference of Two Squares
Perfect Square Trinomials
x  10 x  16 
x  8 x  16 
2
2

 x
x  4x  4
2
x  4
x


x

x
x  2x  8
Not a perfect square

11.5 – Factoring Perfect Square Trinomials
and the Difference of Two Squares
Perfect Square Trinomials
x  18 x  81 
2

 x

 x  9 x  9
x
x  9
2
9 x  42 x  49 
x
 x

2

3x  7 3x  7 
3x  7 
2
11.5 – Factoring Perfect Square Trinomials
and the Difference of Two Squares
The Difference of Two Squares
9s  1 
 3s  13s 1
p  81 
 p  9 p  9
2
2
4 x  100  Not the difference
2
11.5 – Factoring Perfect Square Trinomials
and the Difference of Two Squares
The Difference of Two Squares
121x  49 y 
2
2
11x  7 y 11x  7 y 
9
3 
3

64c 
  8c    8c  
25 
5 
5
2
11.5 – Factoring Perfect Square Trinomials
and the Difference of Two Squares
The Difference of Two Squares
48 x  3 
4
3 16 x  1 
4
3  4 x  1 4 x  1
2
2
3  4 x  1  2 x  1 2 x  1
2
p  13 
2
p
13
 p 
13
