11.3 - Factoring General Trinomials Factoring Trinomials REVIEW: x bx c 4 x 24 x 36 4 x
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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 4x 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 4x 4
2
x 4
x
x
x
x 2x 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 13s 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